Prove the following identity: from Mathematics Introduction to
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    Introduction to Trigonometry

    Multiple Choice QuestionsShort Answer Type

    371. Prove the following identity:
    fraction numerator sinA minus sinB over denominator cosA plus cosB end fraction plus fraction numerator cosA minus cosB over denominator sinA plus sinB end fraction equals 0.
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    372. Prove the following identity:
    tan squared straight A minus tan squared straight B space equals space fraction numerator sin squared straight A minus sin squared straight B over denominator cos squared straight A cross times cos squared straight B end fraction.
    117 Views
    Answer
    373. Prove the following identity:
    left parenthesis secA minus tanA right parenthesis squared space left parenthesis 1 plus sinA right parenthesis space equals space 1 minus space sinA.
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    Answer
    374. Prove the following identity:
    sec to the power of 6 straight theta space equals space tan to the power of 6 straight theta space plus space 3 space tan space straight theta. space secθ plus 1
    103 Views
    Answer
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    375. Prove the following identity:
    left parenthesis 1 plus tan squared straight theta right parenthesis plus open parentheses 1 plus fraction numerator 1 over denominator tan squared straight theta end fraction close parentheses space equals fraction numerator 1 over denominator sin squared straight theta minus sin to the power of 4 straight theta end fraction
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    376. Prove the following identity:
    left parenthesis 1 plus tanA. tanB right parenthesis squared plus left parenthesis tanA minus tanB right parenthesis squared space equals sec squared straight A. space sec squared straight B.
    93 Views
    Answer
    377. Prove the following identity:
    cotθ minus tanθ space equals space fraction numerator 2 space cos squared straight theta minus 1 over denominator sinθ minus cosθ end fraction.
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    Answer
    378. Prove the following identity:
    tan squared straight theta plus cot squared straight theta plus 2 space equals space sec squared straight theta. space cosec squared straight theta.
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    Answer
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    Multiple Choice QuestionsLong Answer Type

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    379. Prove the following identity:
    left parenthesis 1 plus cotA plus tanA right parenthesis space left parenthesis sinA minus cosA right parenthesis space equals space sinA. space tanA minus space cotA. space cosA.

    L.H.S. = (1+ cot A + tan A) (sin A - cos A)
    equals open parentheses 1 plus cosA over sinA plus sinA over cosA close parentheses space left parenthesis sinA minus cosA right parenthesis equals space open parentheses 1 plus fraction numerator cos squared straight A plus sin squared straight A over denominator sinA space cosA end fraction close parentheses space left parenthesis sinA minus cosA right parenthesis equals open parentheses 1 plus fraction numerator 1 over denominator sinA space cosA end fraction close parentheses space left parenthesis sinA space minus space cosA right parenthesis equals space open parentheses fraction numerator sinA. space cosA space plus 1 over denominator sinA space cosA end fraction close parentheses space left parenthesis sinA space minus space cosA right parenthesis equals space fraction numerator left parenthesis sinA minus cosA right parenthesis space left parenthesis 1 plus sinA space cosA right parenthesis over denominator sinA space cosA end fraction straight R. straight H. straight S. space equals space sinA. space tanA space minus space cotA space cosA
    equals space sinA. space sinA over cosA minus cosA over sinA. cosA equals space fraction numerator sin squared straight A over denominator cosA end fraction minus fraction numerator cos squared straight A over denominator sinA end fraction equals fraction numerator sin cubed straight A minus cos cubed straight A over denominator sinA space cosA end fraction equals space fraction numerator left parenthesis sinA minus cosA right parenthesis space left parenthesis sin squared straight A plus cos squared straight A plus sinA. space cosA right parenthesis over denominator sinA. space cosA end fraction equals space fraction numerator left parenthesis sinA minus cosA right parenthesis left parenthesis 1 plus sinA space cosA right parenthesis over denominator sinA. cosA end fraction

    L.H.S. = R.H.S.
    Hence, (1 + cot A + tan A) (sin A - cos A) = sin A . tan A - cot A . cos A Proved

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    Multiple Choice QuestionsShort Answer Type

    380. If 7 sin2θ + 3cos2θ = 4, show that tanθ space equals space fraction numerator 1 over denominator square root of 3 end fraction.
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