Simplify it - 1-sin-1-sin-1-cos-1-cos-

We have, #10; #10; ( 1+sinθ #160; )( 1 sinθ #160; )( 1+cosθ #160; )( 1 cosθ #160; ) #10; #10; =1 sin^2θ1 cos^2θ #10; #10; =cos ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Cos(A+B)Cos(A-B)

Simplify it :...

Question

Simplify it :-
$\frac{(1 + sin θ) (1 - sin θ)}{(1 + cos θ) (1 - cos θ)}$

Open in App

Solution

Suggest Corrections

Similar questions

If tan (A + B) = \sqrt{3}; tan (A - B) = \frac{1}{\sqrt{3}}

\frac{(1 + sin θ) (1 - sin θ)}{(1 + cos θ) (1 - cos θ)}

sin θ (1 + sin θ) + cos θ (1 + cos θ) = x

sin θ (1 - sin θ) + cos θ (1 - cos θ) = y

\sqrt{\frac{\sec θ - 1}{\sec θ + 1}} + \sqrt{\frac{\sec θ + 1}{\sec θ - 1}} = 2 cosec θ

\sqrt{\frac{1 + \sin θ}{1 - \sin θ}} + \sqrt{\frac{1 - \sin θ}{1 + \sin θ}} = 2 \sec θ

\sqrt{\frac{1 + \cos θ}{1 - \cos θ}} + \sqrt{\frac{1 - \cos θ}{1 + \cos θ}} = 2 cosec θ

\frac{\sec θ - 1}{\sec θ + 1} = {(\frac{\sin θ}{1 + \cos θ})}^{2}

\frac{\sin θ + 1 - \cos θ}{\cos θ - 1 + \sin θ} = \frac{1 + \sin θ}{\cos θ}

(i) \sqrt{\frac{1 + \sin θ}{1 - \sin θ}} = (\sec θ + \tan θ) (ii) \sqrt{\frac{1 - \cos θ}{1 + \cos θ}} = (cosec θ - \cot θ) (iii) \sqrt{\frac{1 + \cos θ}{1 - \cos θ}} + \sqrt{\frac{1 - \cos θ}{1 + \cos θ}} = 2 cosec θ

cot θ = \frac{7}{8}

\frac{(1 + sin θ) (1 - sin θ)}{(1 + cos θ) (1 - cos θ)}

Join BYJU'S Learning Program