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Introduction to Trigonometry

Short Answer Type

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

87 Views

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

102 Views

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

123 Views

Long Answer Type

84. Given that

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what is the value of

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160 Views

85.

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

142 Views

Short Answer Type

86.

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

89 Views

87.

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

135 Views

88.

If $cotθ space equals space 15 over 8 comma$ then evaluate "<pre

95 Views

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.

We have,
A + B = 90°

rightwards double arrow space space straight A space equals space 90 degree minus straight B

...(i)
Now,

secA space equals space 15 over 7

rightwards double arrow space space space sec left parenthesis 90 degree minus straight B right parenthesis space equals space 15 over 17 space space space space space space space space left square bracket using space left parenthesis straight i right parenthesis right square bracket rightwards double arrow space space space space space space space space space space space space cosecB space equals space 15 over 7 Ans. space

111 Views

90.

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