Question

find value of sin15 + tan15?

Answer 1

Answer:

sin15 = (sin(45-30))

use formula sin(A-B) = sinA.cosA - cosA.sinB

to find sin15

sin15 = sin(45-30) = sin45.cos30 - cos45.sin30

→ 1/√2 x √3/2 - 1/√2 x 1/2

→ √3/2√2 - 1/2√2

→ (√3 - 1)/2√2

sin15 = (√3-1)/2√2

similarly now find tan15

tan(A-B) = (tanA - tanB)/1+tanA.tanB

tan15 = tan(45-30) = (tan45 - tan30)/1+tan45.tan30

tan15 = (1-1/√3)/(1+1/√3)

tan15 = ((√3-1)/√3)/(√3+1)/√3 = (√3-1)/(√3+1)

sin15 + tan15

= (√3-1)/2√2 + (√3-1)/(√3+1)

add them you will get your answer.

hope this will help you