Question

1+ tan square theta × 1- sin theta whole square equal to 1​

Answer 1

Question:

$\rightarrowtail \bold{Prove\;that\;(1+tan^{2}\theta)(1-sin\theta)(1+sin\theta)=1}$

Solution:

• 1 + tan²Ф = sec²Ф

$\mapsto \bold{sec^{2}\theta (1-sin\theta)(1+sin\theta)}$

• (a + b)(a - b) = a² - b²

$\mapsto \bold{sec^{2}\theta(1^{2}-sin^{2}\theta)}$

• 1 - sin²Ф = cos²Ф

$\mapsto \bold{sec^{2}\theta \;cos^{2}\theta}$

• secФ = 1/cosФ

$\mapsto \bold{\dfrac{1}{cos^{2}\theta}\times cos^{2}\theta }$

$\Rrightarrow \bold{1}$

• ∴ L.H.S = R.H.S