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202. If A, B, C are interior angles of a triangle ABC, prove that

tan open parentheses fraction numerator straight B plus straight C over denominator 2 end fraction close parentheses equals space space cot straight A over 2.

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203. If A, B, C are interior angles of a triangle ABC. Prove that cot

open parentheses fraction numerator straight B plus straight C over denominator 2 end fraction close parentheses equals space space tan straight A over 2.

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204. If A, B, C are interior angles of a triangle ABC. Prove that

cos open parentheses fraction numerator straight A plus straight C over denominator 2 end fraction close parentheses space equals space sin straight B over 2.

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205. If A, B, C are interior angles of a

increment ABC

Prove that

sec open parentheses fraction numerator straight A plus straight B over denominator 2 end fraction close parentheses space equals space cosec straight C over 2.

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206. If A, B, C are interior angles of a ΔABC, show that
(i)

sin space fraction numerator straight B plus straight C over denominator 2 end fraction equals space cos straight A over 2.

(ii)

cos fraction numerator straight B plus straight C over denominator 2 end fraction equals sin straight A over 2.

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207. If A, B, C are interior angles of a ΔABC, show that
(i)

cos squared straight A over 2 plus cos squared open parentheses fraction numerator straight B plus straight C over denominator 2 end fraction close parentheses equals 1.

(ii)

1 plus tan squared open parentheses fraction numerator straight B plus straight C over denominator 2 end fraction close parentheses space equals space cosec squared straight A.

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208. Evaluate:
(i) tan (55° - θ) - cot (35° + θ)
(ii) cosec (65° + θ) - sec (25° - θ)

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209. Prove the following identities:
tan θ + cot θ = sec θ. cosec θ

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210. Prove the following identities:

fraction numerator tanθ plus sinθ over denominator tanθ minus sinθ end fraction equals fraction numerator secθ plus 1 over denominator secθ minus 1 end fraction

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