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231. Prove the following identities:

fraction numerator cos squared straight theta over denominator 1 minus tanθ end fraction plus fraction numerator sin cubed straight theta over denominator sinθ minus cosθ end fraction equals 1 plus sinθ. space cosθ

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232. Prove the following identities:
(sin θ - sec θ)² + (cos θ - cosec θ) = (1 - sec θ. cosec θ)²

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233. Evaluate:
sin 63°. cos 27° + cos 63° . sin 27°

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234. Evaluate:

fraction numerator sin squared 20 degree plus sin squared 70 degree over denominator cos squared 20 degree plus cos squared 70 degree end fraction plus fraction numerator sin left parenthesis 90 degree minus straight theta right parenthesis. sinθ over denominator tanθ end fraction plus fraction numerator cos left parenthesis 90 degree minus straight theta right parenthesis. space cosθ over denominator cotθ end fraction

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235. Evaluate:

cosθ. space sinθ space minus space fraction numerator sinθ. space cos left parenthesis 90 degree minus straight theta right parenthesis. space cosθ over denominator sec left parenthesis 90 degree minus straight theta right parenthesis end fraction minus fraction numerator cosθ. space sin left parenthesis 90 degree minus straight theta right parenthesis. space sinθ over denominator cosec left parenthesis 90 degree minus straight theta right parenthesis end fraction

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236. Evaluate:

cos left parenthesis 40 degree plus straight theta right parenthesis space minus space sin left parenthesis 50 degree minus straight theta right parenthesis plus fraction numerator cos squared 40 degree plus cos squared 50 degree over denominator sin squared 40 degree plus sin squared 50 degree end fraction

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237. Evaluate:

fraction numerator cos squared 20 degree plus cos squared 70 degree over denominator sin squared 59 degree plus sin squared 31 degree end fraction plus sin space 35 degree. space sec space 55 degree.

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238. Evaluate:
sin 47°. cos 43° + cos 47° . sin 43°

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Solution not provided.
Ans. -2

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240. Evaluate:
sin 35°.cos 55° + cos 35°. sin 55°

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