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Introduction to Trigonometry

Short Answer Type

161.

If $sin space straight theta space equals space 3 over 4 comma$ prove that : $square root of fraction numerator cosec squared straight theta minus 1 over denominator sec squared straight theta minus 1 end fraction end root space equals space fraction numerator square root of 7 over denominator 3 end fraction.$

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162.

Evaluate the following:
sin 60°. cos 45° + cos 60° sin 45°

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163.

Evaluate the following:
sin 30°. cos 45° + cos 30° sin 45°

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164.
Evaluate the following:
3 cos² 30° + sec² 30° + 2 cos 0° + 3 sin 90° - tan² 60°

Solution not provided.
Ans. $67 over 12 semicolon$

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165.

Evaluate the following:
sin² 60° + sec² 30° + sin 90° + 3 cos 0° - tan² 60°

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166.

Evaluate the following:
$fraction numerator 4 space sin space 30 degree space plus space cos squared 45 degree minus 4 cos squared 60 degree over denominator 2 space sin space 30 degree. space cosec space 30 degree plus tan squared 45 degree end fraction.$

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167. If cos (A - B) = 1, sin (A + B) = 1. Find A and B.

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168. If tan (A + B) = 1, tan (A - B) = 1. Find A and B.

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169.

If $sin left parenthesis straight x minus straight y right parenthesis space equals space 1 half space and space cos left parenthesis straight x plus straight y right parenthesis space equals space 1 half.$ Find x and y.