Question

if (1+sina)(1+cosa)=5/4 then the value of (1-sina)(1-cosa) is equal to

Answer 1

Hi ,

( 1 + sinA ) ( 1 + cosA ) = 5/4

Multiply both sides with

( 1 - sinA ) ( 1 - cosA )

( 1 - sin²A ) ( 1 - cos² A ) = 5/4 ( 1-sinA)(1-cosA)

Cos² A sin²A = 5/4 ( 1-sina) ( 1- cosA)

Therefore ,

( 1-sinA) (1 - cosA ) = 4/5(cos²A sin² A)

I hope this helps you.

:)

Answer 2

$\huge\sf\blue{Given}$

✭ (1 + sinα)(1 + cosα) = \sf \dfrac{5}{4}

$\rule{110}1$

$\sf{\underline{\bullet{ Identities \:used}}}$

1 - sin²θ = cos²θ

1 - cos²θ = sin²θ

(a + b)(a - b) = a² - b²

$\rule{100}1$

$\huge\sf\purple{Steps}$

❍ On multiplying both sides by (1 - sinα)(1 - cosα)

➳[(1 + sinα)(1 + cosα)}{(1 - sinα)(1 - cosα)]=$\sf \dfrac{5}{4}$ × (1 - sinα)(1 - cosα)

➳ (1 - sin²α)(1 - cos²α) = $\sf \dfrac{5}{4}$ × (1 - sinα)(1 - cosα)

➳ cos²α * sin²α = $\sf \dfrac{5}{4}$× (1 - sinα)(1 - cosα)

➳ (1 - sinα)(1 - cosα) = $\sf \dfrac{4}{5}$( cos^α sin^2α )

$\rule{170}3$