Question

Cos/1-sin+cos/1+sin=4

Answer 1

simplify it then replace ø by 60° then 4 will come as answer

Answer 2

$\dfrac{\cos A}{1-\sin A}+\dfrac{\cos A}{1+\sin A}=4,$ proved.

Step-by-step explanation:

Prove that, $\dfrac{\cos A}{1-\sin A}+\dfrac{\cos A}{1+\sin A}=4$.

L.H.S.$=\dfrac{\cos A}{1-\sin A}+\dfrac{\cos A}{1+\sin A}$

$=\dfrac{\cos A(1+\sin A)+\cos A(1-\sin A)}{(1-\sin A)(1+\sin A)}$

$=\dfrac{\cos A+\cos A\sin A+\cos A-\cos A\sin A}{(1-\sin A)(1+\sin A)}$

$=\dfrac{\cos A+\cos A}{1^-\sin^2 A}$

Using algebraic identity,

$(a+b(a-b)=a^{2} -b^{2}$

$=\dfrac{2\cos A}{\cos^2 A}$

Using trigonometric identity,

$\cos^2 A=1-\sin^2 A$

$=\dfrac{2}{\cos A}$

$=2\sec A$

Using trigonometric identity,

$\sec A=\dfrac{1}{\cos A}$

Put A = 60°

[tex]=2\sec 60 =2\times 2[/tex]

= 4 = R.H.S., proved.

Hence, $\dfrac{\cos A}{1-\sin A}+\dfrac{\cos A}{1+\sin A}=4,$ proved.