Question

Prove that (1+tan^ theta)(1-sin theta)(1+sin theta )=1​

Answer 1

Answer:

See explanation

Step-by-step explanation:

  $(1+\tan^2\theta)(1-\sin\theta)(1+\sin\theta)$

  $=(\sec^2\theta)(1^2-\sin^2\theta)$

• Since $(a-b)(a+b)=a^2-b^2$ and $\sec^2\theta-\tan^2\theta=1$

  $=\sec^2\theta\times (1-\sin^2\theta)\\=\sec^2\theta\cos^2\theta$

• Since $\sin^2\theta+\cos^2\theta=1$

  $=(\sec\theta\cos\theta)^2=1^2=1$

Hence proved