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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    Answer
    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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    Answer
    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
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    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.

    tan squared straight theta plus cot squared straight theta plus 2 equals sec squared straight theta. space cosec squared straight theta
    L.H.S. = tan squared straight theta plus cot squared straight theta plus 2
               equals space fraction numerator sin squared straight theta over denominator cos squared straight theta end fraction plus fraction numerator cos squared straight theta over denominator sin squared straight theta end fraction plus 2
                equals space fraction numerator sin to the power of 4 straight theta plus cos to the power of 4 straight theta plus 2 sin squared straight theta. space cos squared straight theta over denominator cos squared straight theta. space sin squared straight theta end fraction equals space fraction numerator left parenthesis sin squared straight theta right parenthesis squared plus left parenthesis cos squared straight theta right parenthesis squared plus 2 sin squared straight theta. space cos squared straight theta over denominator blank end fraction equals space fraction numerator left parenthesis sin squared straight theta plus cos squared straight theta right parenthesis squared over denominator cos squared straight theta. space sin squared straight theta end fraction space equals fraction numerator 1 over denominator cos squared straight theta. space sin squared straight theta end fraction equals space sec squared straight theta. space cosec squared straight theta space equals space straight R. straight H. straight S.
    Hence, L.H.S. = R.H.S.
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    Multiple Choice QuestionsLong Answer Type

    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.
    519 Views
    Answer

    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.
    235 Views
    Answer
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