Question

If sinA=1/√5 and sinB=1/√10, then find the value of cos A and cosB.
hence using the formula cos(A+B) = cosA.cosB-sinA.sinB, show that A+B=45o

Answer 1

sinA =1/√5
cosA=√(1-sin²A) (sin²A+cos²A=1)
=√1-1/√5² (1-cos²A=sin²A
=√1-1/5. (cosA=√1-sin²A)
=√5-1/5
=√4/5
cosA=2/√5
sinB =1/√10
cosB=√1-sin²B
=√1-1/√10²
=√1-1/10
=√10-1/10
=√9/10
cosB=3/√10
Cos(A+B)=cosA. cosB-sinA. sinB
=2/√5 x 3/√10 - 1/√5 x 1/√10
=6/√50-1/√50
=5/√50
=5/5√2
=1/√2
cos(A+B)=1/√2
Cos(A+B)=Cos 45
A+B=45
SHOWN..

Answer 2

Answer:

If sin A = and sin B = cos A and cos B.Hence using the formula

cos (A +B) = cos A .cos B – sin A .sin B show that A + B = 45.