Can someone help me prove 8 a,b, and c

Question

asked Dec 12, 2023 106k views

1 Answer

Yuri Baburov · Answer 1 · 2023-12-16T19:27:02+0000

Explanation:

8) Consider,

$(1)/(1 + \sin(x) )$

Multiplying And Dividing By 1-sinx

$(1)/(1 + \sin(x) ) * (1 - \sin(x) )/(1 - \sin(x) )$

$(1 - \sin(x) )/((1 + \sin(x) )(1 - \sin(x)) )$

We know (a+b)(a-b)=a²-b²

$(1 - \sin(x) )/(1 - \sin ^(2) (x) )$

We know that sin²x+cos²x=1

cos²x=1-sin²x,

uisng this we get,

$(1 - \sin(x) )/( \cos ^(2) (x) )$

$(1)/( \cos ^(2) (x) ) - ( \sin(x) )/(cos ^(2) (x))$

We know that 1/cosx=secx and sinx/cosx=tanx

Using this we get,

$\sec {}^(2) (x) - ( \tan(x) )/( \cos(x) )$

Hence Proved