Question

8. In a right-angled triangle ABC, the right angle is at B. If tan A= √3, then find the value of (i) sin A cos C + cos A sin C (ii) cos A cos C-sin A sin C
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Answer 1

ǫᴜᴇsᴛɪᴏɴ →

8. In a right-angled triangle ABC, the right angle is at B. If tan A= √3, then find the value of (i) sin A cos C + cos A sin C (ii) cos A cos C-sin A sin C

ᴀɴsᴡᴇʀ →

In △ABC,∠B=90 o tanA= 3/1 = AB BC

Let BC =1x,AB= 3 x

AC² = AB2+BC2

AC² =( 3x) 2+(x) 2 =4x2

AC=2x

(i) sinAcosC+cosAsinC= 2/1 × 2/1 + 2/3 × 2/3 = 4/1 + 4/3 = 1

(ii) cosAcosC−sinAsinC= 2/3 × 2/1 − 2/1 × 2/3 = 4/3 − 4/3 = 0