Question

IN A TRIANGLE ABC RIGHT ANGLED AT B , ANGLE A =ANGLE C FIND THE VALUE OF


1) SINA.COSC + COSA.SINC

2) SINA.SINB + COS A.COSB

Answer 1

is tarike se v to ban skta hai na...

Answer 2

Given: In triangle ABC

Angle B=90 degree

Angle A=Angle C

To find:

(1) SinA Cos C+Cos ASin C

(2) SinASin B+CosA Cos B

Solution:

In triangle ABC

$\angle A+\angle B+\angle C=180^{\circ}$

Using triangle angles sum property

Substitute the values

$\angle A+90+\angle A=180$

$2\angle A=180-90=90$

$\angle A=\frac{90}{2}=45^{\circ}$

$\angle A=\angle C=45^{\circ}$

(1)

$Sin 45Cos 45+Cos 45Sin 45$

$\frac{1}{\sqrt 2}\times \frac{1}{\sqrt 2}+\frac{1}{\sqrt 2}\times \frac{1}{\sqrt 2}$

$\frac{1}{2}+\frac{1}{2}=\frac{1+1}{2}=\frac{2}{2}$

$=1$

(2)

$Sin 45Sin90+Cos45Cos 90$

$\frac{1}{\sqrt 2}\times 1+\frac{1}{\sqrt 2}\times 0$

$\frac{1}{\sqrt 2}$