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181. If A = 30° and B = 60°, verify that
cos (A + B) = cos A . cos B - sin A . sin B.

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Solution not provided.
Ans. $45 degree$

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183. If θ = 30°, verify that

tan space 2 straight theta space equals space fraction numerator 2 space tanθ over denominator 1 minus tan squared straight theta end fraction

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184. If θ = 30°, verify that
cos 3θ = 4 cos³θ - 3 cosθ.

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185. If θ = 30°, verify that

sin space 2 straight theta space equals space fraction numerator 2 tanθ over denominator 1 minus tan squared straight theta end fraction

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186. If θ = 30°, verify that

cos space 2 straight theta space equals space fraction numerator 1 minus tan squared straight theta over denominator 1 plus tan squared straight theta end fraction.

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187. Evaluate:

fraction numerator sin space 70 degree over denominator cos space 20 degree end fraction plus fraction numerator cos space 20 degree over denominator sin space 70 degree end fraction minus 2 space cos space 70 degree. space cosec space 20 degree.

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188. Evaluate:

fraction numerator cos space 70 degree over denominator sin space 20 degree end fraction plus fraction numerator cos space 55 degree cross times cosec space 35 degree over denominator tan space 5 degree cross times tan space 25 degree cross times tan space 45 degree cross times tan space 65 degree cross times tan space 55 degree end fraction

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189. Evaluate:

2 open parentheses fraction numerator cos squared 20 degree plus cos squared 70 degree over denominator sin squared 25 degree plus sin squared 65 degree end fraction close parentheses minus tan 45 degree plus tan 13 degree. space tan 23 degree. space tan space 30 degree. space tan space 67 degree comma space tan 77 degree.

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190. Evaluate:

fraction numerator cos space 70 degree over denominator sin space 20 degree end fraction plus fraction numerator cos space 59 degree over denominator sin space 31 degree end fraction minus 8 space sin squared 30.

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