Question

Prove that root 1 - sin square 90 - theta + root 4 - 4 sin square 90 - theta equals to 3 sin theta

Answer 1

hope it's help u..... ..

Answer 2

$\Rightarrow LHS=3\ sin\ \theta=RHS$ hence proved

Explanation:

To prove:

$\sqrt{1-sin^2 (90-\theta)} +\sqrt{4-4\ sin^2 (90-\theta)} =3\ sin\ \theta$

Now,

$\Rightarrow LHS=\sqrt{1-cos^2\ \theta} + \sqrt{4(1-sin^2\ \theta)}$

$\Rightarrow LHS=\sqrt{sin^2\ \theta} +2\sqrt{sin^2\ \theta}$

$\Rightarrow LHS=sin\ \theta+2\ sin\ \theta$

$\Rightarrow LHS=3\ sin\ \theta=RHS$

hence proved.

Trigonometric results used:

• $sin\ (90-\theta)=cos\ \theta$

• $sin^2\ \theta+cos^2\ \theta=1$

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TOPIC: trigonometry

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