Question

5.Find the value of:(i) sin 75(ii) tan 15°

Answer 1

(i).

Use trigonometric function sin( A+B )=sinA⋅cosB+cosA⋅sinB

sin( 75° )=sin( 45°+30° ) =sin45°⋅cos30°+cos45°⋅sin30° =( 1 2 )( 3 2 )+( 1 2 )( 1 2 ) = 3 2 2 + 1 2 2 = 3 +1 2 2

Thus, sin( 75 ∘ ) is equal to 3 +1 2 2 .

(ii).

Use trigonometric function tan( A−B )= tanA−tanB 1+tanA⋅tanB

tan( 15° )=tan( 45°−30° ) = tan45°−tan30° 1+tan45°⋅tan30° = 1− 1 3 1+1( 1 3 ) = 3 −1 3 3 +1 3

Simplify above expression.

= 3 −1 3 +1 = ( 3 −1 ) 2 ( 3 +1 )( 3 −1 ) = 4−2 3 3−1 =2− 3

Thus, tan( 15 ∘ ) is equal to 2− 3 .