Question

Find the value of sqrt 1-cos^ 2 theta 1-sin^ 2 theta if theta=30.​

Answer 1

Answer:

First we take left side and put \theta=30^{\circ}θ=30

∘

\Rightarrow \cos2(30^{\circ})⇒cos2(30

∘

)

\Rightarrow \cos60^{\circ}⇒cos60

∘

\Rightarrow \dfrac{1}{2}⇒

2

1

Now we take right side and put \theta=30^{\circ}θ=30

∘

\Rightarrow \dfrac{1-\tan^2\theta}{1+\tan^2\theta}⇒

1+tan

2

θ

1−tan

2

θ

\Rightarrow \dfrac{1-\tan^230^{\circ}}{1+\tan^230^{\circ}}⇒

1+tan

2

30

∘

1−tan

2

30

∘

\Rightarrow \dfrac{1-\frac{1}{3}}{1+\frac{1}{3}}⇒

1+

3

1

1−

3

1

\Rightarrow \dfrac{3-1}{3+1}⇒

3+1

3−1

\Rightarrow \dfrac{1}{2}⇒

2

1

LHS=RHS=\dfrac{1}{2}LHS=RHS=

2

1

Hence verified