Express the trigonometric ratios sin A sec A, and tan A in terms
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    Introduction to Trigonometry

    Multiple Choice QuestionsShort Answer Type

    31. If tan 2A = cot (A - 18°), where 2A is an acute angle, find the value of A.
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    32. If tan A = cot B, prove that A + B = 90°. 
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    33. If sec 4A = cosec (A - 20°), where 4A is an acute angle, find the value of A.
    184 Views
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    34. If A, B and C are interior angles of ΔABC, then show that
              space sin space open parentheses fraction numerator straight B plus straight C over denominator 2 end fraction close parentheses space equals space cos straight A over 2.
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    35. Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.
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    36. Express the trigonometric ratios sin A sec A, and tan A in terms of cot A.

    cot squared straight A space plus space 1 space equals cosec squared straight A
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    Hence,      sinA space equals space 1 over cosecA equals fraction numerator 1 over denominator square root of cot squared straight A plus 1 end root end fraction
                     secA space equals space 1 over cosA space equals space cosecA over cotA

                                equals space fraction numerator square root of cot squared straight A plus 1 end root over denominator cotA end fraction
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    Multiple Choice QuestionsLong Answer Type

    37. Write all the other trigonometric ratios of ∠A in terms of sec A.
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    Multiple Choice QuestionsShort Answer Type

    38. Evaluate:
    fraction numerator sin squared 63 degree plus sin squared 27 degree over denominator cos squared 17 degree plus cos squared 73 degree end fraction.
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    39. Evaluate:
    sin space 25 degree. space cos space 65 degree space plus space cos space 25 degree space. space sin space 65 degree.
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    40. Choose the correct option and Justify your choice.
    9 sec2A - 9 tan2A =
    (A) 1    (B)    9    (C)    8       (D) 0
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