Question

if cos2A= 7/8, show that sinA=1/4​

Answer 1

Answer:

In Δ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine:

(i) sin A, cos A (ii) sin C, cos C

Answer:

Class_10_Introduction_To_Trigonometry_RightAngledTriangleABC6

In Δ ABC, by Pythagoras theorem,

AC2 = AB2 + BC2

=> AC2 = 242 + 72

=> AC2 = 576 + 49

=> AC2 = 625

=> AC = √625

=> AC = 25

(i) sin A = BC/AC = 7/25, cos A = AB/AC = 24/25

(ii) sin C = AB/AC = 24/25, cos C = BC/AC = 7/25

Answer 2

Answer:

solution:

given, cos 2A=7

using formula,

cos 2A =1-2sin^2A

7/8=1-2sin^2A

7/8-1=2sin^2A

1/8=2sin^2A

(1/4)^2=(sinA)^2

∴ sinA=1/4 proved

Step-by-step explanation: