If sin A = frac{1}{sqrt{10}} and sin B = frac | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given that $A$ and $B$ are positive and acute angles $(0 < A, B < 90^{\circ})$.Since $\sin A = \frac{1}{\sqrt{10}}$,then $\cos A = \sqrt{1 - \sin^

Vedclass · Accepted Answer

$\frac{\pi}{4}$

Vedclass · Answer

(B) Given that $A$ and $B$ are positive and acute angles $(0 Since $\sin A = \frac{1}{\sqrt{10}}$,then $\cos A = \sqrt{1 - \sin^2 A} = \sqrt{1 - \frac{1}{10}} = \sqrt{\frac{9}{10}} = \frac{3}{\sqrt{10}}$.Since $\sin B = \frac{1}{\sqrt{5}}$,then $\cos B = \sqrt{1 - \sin^2 B} = \sqrt{1 - \frac{1}{5}} = \sqrt{\frac{4}{5}} = \frac{2}{\sqrt{5}}$.Using the formula $\sin(A + B) = \sin A \cos B + \cos A \sin B$:$\sin(A + B) = \left(\frac{1}{\sqrt{10}}\right) \left(\frac{2}{\sqrt{5}}\right) + \left(\frac{3}{\sqrt{10}}\right) \left(\frac{1}{\sqrt{5}}\right)$$= \frac{2}{\sqrt{50}} + \frac{3}{\sqrt{50}} = \frac{5}{\sqrt{50}} = \frac{5}{5\sqrt{2}} = \frac{1}{\sqrt{2}}$.Since $\sin(A + B) = \frac{1}{\sqrt{2}}$ and $A, B$ are acute,$A + B = \frac{\pi}{4}$.

If $\sin A = \frac{1}{\sqrt{10}}$ and $\sin B = \frac{1}{\sqrt{5}}$,where $A$ and $B$ are positive and acute angles,then $A + B = $

Similar Questions

If $\operatorname{cosec} \theta + \cot \theta = p,$ then $\cos \theta =$

The value of the expression $1 - \frac{\sin^2 y}{1 + \cos y} + \frac{1 + \cos y}{\sin y} - \frac{\sin y}{1 - \cos y}$ is equal to

If $\sin A = \sin B$ and $\cos A = \cos B,$ then

If $\cos (\alpha + \beta ) = \frac{4}{5}, \sin (\alpha - \beta ) = \frac{5}{13}$ and $\alpha, \beta$ lie between $0$ and $\frac{\pi}{4}$,then $\tan 2\alpha = $

If $A$ and $B$ are complementary angles,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module