Question

1
The value of
2 sin 10°
- 2 sin 70° is​

Answer 1

Step-by-step explanation:

(1 - 4 sin 70 * sin 10) / (2 sin 10) (Taking L.C.M.)

= (1 - 2 * 2 sin 70 * sin 10 ) / (2 sin 10) (Writing 4 = 2 * 2)

= [ 1 - 2 { cos (70 - 10) - cos ( 70 + 10)}] / ( 2 sin 10) ( Using 2 sin A * sin B = cos ( A - B) - cos ( A + B) )

= [ 1 - 2 { cos 60 - cos 80}] / { 2 sin ( 90 - 80)} ( Writing 10 = 90 - 80)

= [ 1 - 2 { 1/2 - cos 80}] / (2 cos 80) ( As sin (90 - A) = cos A)

= [1 - 1 + 2 cos 80] / (2 cos 80) ( Opening curly bracket in numerator )

= (2 cos 80) / ( 2 cos 80)

= 1

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