Question

In a ΔABC right angled at B,∠A=∠C . Find the values of
(i)sinAcosC+cosAsinC
(ii)sinAsinB+cosAcosB

Answer 1

Step-by-step explanation:

answer is 1 I hope this helps you

Answer 2

(i) sinA.cosC + cosA.sinC  = 1

(ii) sinA.sinB + cosA.cosB  = = 1/√2

Step-by-step explanation:

Given: In a ΔABC right angled at B, ∠A = ∠C

Find: (i) sinAcosC + cosA sinC

      (ii) sinA sinB + cosA cosB

Solution:

 In ΔABC, ∠B = 90°.

  ∠C= ∠A = 180-90 / 2 = 90/2 = 45°

(i) sinA.cosC + cosA.sinC = Sin45°.cos 45° + Cos45°.Sin45°

 = 1/√2 . 1/√2  +  1/√2 . 1/√2  

 = 1/2 + 1/2

 = 1

 

(ii) sinA.sinB + cosA.cosB = Sin45°.Sin 90° + Cos45°. Cos90°

 = 1/√2. 1 + 1/√2 . 0

 = 1/√2