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Introduction to Trigonometry

Short Answer Type

81. If sin θ = cos θ, find the value of θ.

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82. If tan θ = cot (30° + θ), find the value of θ.

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83. If sin 3θ = cos (θ - 6°) and θ-6° are acute angles, find the value of θ.

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Long Answer Type

84. Given that

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what is the value of

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85.

If $tanθ space equals space 4 over 3 comma$ what is the value of $fraction numerator sinθ plus cosθ over denominator sinθ minus cosθ end fraction ?$

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Short Answer Type

86.

If $space tanA space equals space 5 over 12 comma$ find the value of (sinA + cosA) secA.

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87.

If $cosA space equals space 7 over 25 comma$ find the value of (tanA + cotA).

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88.
If $cotθ space equals space 15 over 8 comma$ then evaluate

fraction numerator left parenthesis 2 plus 2 sinθ right parenthesis thin space left parenthesis 1 minus sinθ right parenthesis over denominator left parenthesis 1 plus cosθ right parenthesis thin space left parenthesis 2 minus 2 cosθ right parenthesis end fraction equals space fraction numerator 2 left parenthesis 1 plus sinθ right parenthesis thin space left parenthesis 1 minus sinθ right parenthesis over denominator 2 left parenthesis 1 plus cosθ right parenthesis space left parenthesis 1 minus cosθ right parenthesis end fraction equals space fraction numerator 1 minus sin squared straight theta over denominator 1 minus cos squared straight theta end fraction space equals space fraction numerator cos squared straight theta over denominator sin squared straight theta end fraction space equals space cot squared straight theta equals space open parentheses 15 over 8 close parentheses squared space equals space 225 over 64 space Ans. space

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89.

If $secA space equals space 15 over 7 space and space straight A plus straight B space equals space 90 degree comma space$ find the value of cosec B.

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90.

Evaluate:
$fraction numerator sec left parenthesis 90 degree minus straight theta right parenthesis times cosecθ space minus space tan left parenthesis 90 degree minus straight theta right parenthesis space cotθ plus left parenthesis cos squared 35 degree plus cos squared 55 degree right parenthesis over denominator tan 5 degree space tan space 15 degree space tan space 45 degree space tan space 75 degree space tan space 85 degree end fraction.$

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Previous Year Papers

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Short Answer Type

Long Answer Type

Short Answer Type

88. If then evaluate

88.
If $cotθ space equals space 15 over 8 comma$ then evaluate