Question

root 1-cos theta /1+cos theta = sin theta by 1 plus cos theta

Answer 1

Step-by-step explanation:

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Answer 2

Concept:

To prove the given trigonometric identity we have to derive RHS from LHS.

Given:

The given trigonometric identity is $\sqrt{\frac{1-\cos\theta}{1+\cos\theta}}=\frac{\sin\theta}{1+\cos\theta}$.

Find:

Prove the above trigonometric relation.

Solution:

given trigonometric identity is $\sqrt{\frac{1-\cos\theta}{1+\cos\theta}}=\frac{\sin\theta}{1+\cos\theta}$.

LHS =

$\sqrt{\frac{1-\cos\theta}{1+\cos\theta}}$

$=\sqrt{\frac{(1-\cos\theta)(1+\cos\theta)}{(1+\cos\theta)(1+\cos\theta)}}$, multiplying the required with numerator and denominator

$=\sqrt{\frac{1-\cos^2\theta}{(1+\cos\theta)^2}}$, using algebraic identity $(a+b)(a-b)=a^2-b^2$

$=\frac{\sqrt{\sin^2\theta}}{1+\cos\theta}$, since $\sin^2A+\cos^2A=1$ by trigonometric identity

$=\frac{\sin\theta}{1+\cos\theta}$ = RHS

Hence it is proved that $\mathbf{\sqrt{\frac{1-\cos\theta}{1+\cos\theta}}=\frac{\sin\theta}{1+\cos\theta}}$.

#SPJ2