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(cosec A – sin A)(sec A – cos A) = 1/(tan A + cot A)ġ0. Prove that: (cosec A – sin A)(sec A – cos A) = 1/(tan A + cot A) Using the identity cosec 2A = 1 + cot 2A ⇒ cosec 2A – cot 2A = 1,

= (cot A – 1 + cosec A)/(cot A + 1 – cosec A) LHS = (cos A – sin A + 1)/ (cos A + sin A – 1)ĭividing the numerator and denominator by sin A, we get Prove that (cos A – sin A + 1)/ (cos A + sin A – 1) = cosec A + cot A, using the identity cosec 2A = 1 + cot 2A. If tan θ + sec θ = l, prove that sec θ = (l 2 + 1)/2l. If sin 3A = cos (A – 26°), where 3A is an acute angle, find the value of A. Prove that (sin 4θ – cos 4θ +1) cosec 2θ = 2

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