Question

Prove the following identities: i) (1+ tan^2 A) + (1 + 1/ tan^2 A) = 1/ sin^2 A - sin^4 A ii) (cos^2 A -1)(cot^2 A + 1) = -1 iii) (sinTheta + secTheta)^2 + (cosTheta + cosec Theta)^2 = (1 + cosecTheta sec Theta)^2 iv) (1 + cot Theta - cosec Theta)(1 + tan Theta + sec Theta) = 2 v) tan^3 Theta/1 + tan^2 Theta + cot^3 Theta/ 1 + cot^2 Theta = sec Theta cosec Theta - 2 sin Theta cos Theta vi) 1/sec Theta + tan Theta - 1/ cos Theta = 1/ cos Theta - 1/sec Theta - tan Theta vii) sin Theta / 1 + cos Theta + 1 + cos Theta / sin Theta = 2 cosec Theta viii) tan Theta / sec Theta - 1 = sec Theta + 1 /tan Theta ix) cot Theta / cosec Theta - 1 = cosec Theta + 1 / cot Theta x) (sec A + cos A)(sec A - cos A) = tan^2 A + sin^2 A xi) 1+ 3 cosec^2 Theta + cot^6 Theta = cosec^6 Theta xii) 1 - sec Theta + tan Theta / 1 + sec Theta - tan Theta = sec Theta + tan Theta -1/ sec Theta + tan Theta + 1​

Answer 1

Answer:

v

Step-by-step explanation:

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