Question

(iv) ((sin theta + cos theta)² -1)/tan theta-sin theta × cos theta= 2 cot² theta​

Answer 1

Step-by-step explanation:

Let theta is = A

(SinA + CosA)^2 -1/ tanA - SinACosA = 2Cot^2A

Sin^A + Cos^A + 2SinAcosA -1 / tanA - sinAcosA =2cot^2A

1 + 2SinAcosA -1 / sinA/cosA - sinAcosA = 2cot^A

2sinAcosA/ sinA- sinAcos^2A / cosA =2cot^A

2sinAcos^2A/ sinA(1-Cos^2A) =2cot^2A

2sinAcos^2A/ sinA.sin^2A =2Cot^2A

2 cos^2A/ sin^2 A = 2cot^2 A

hence, 2cot^2 A=2 cot^2 A