9.In triangle ABC, right-angled at B, iftan A, find the value of:0 sin

1.	9.In triangle ABC, right-angled at B, iftan A, find the value of:0 sin A cos C+ cos A sin C(i) cos A cos C - sin A sin C
Answer» sin(A+B) = sinA.cosB + cosA.sinB cos(A+B)= cosA. cosB - sinA.sinB Given: tanA=1/√3 A=30° since B is right angle, C=60° Now, sinA.cosC + cosA.sinC =sin(A+C) =sin(30°+60°) =sin90° =1 cosA.cosC - sinA.sinC =cos(A+C) =cos(30°+60°) =cos90° =0

9.In triangle ABC, right-angled at B, iftan A, find the value of:0 sin A cos C+ cos A sin C(i) cos A cos C - sin A sin C

Answer»

sin(A+B) = sinA.cosB + cosA.sinB

cos(A+B)= cosA. cosB - sinA.sinB

Given:

tanA=1/√3

A=30°

since B is right angle, C=60°

Now,

sinA.cosC + cosA.sinC

=sin(A+C)

=sin(30°+60°)

=sin90°

cosA.cosC - sinA.sinC

=cos(A+C)

=cos(30°+60°)

=cos90°