Question

Find the value of: (i) sin 75 Degrees (ii) tan 15 Degrees​

Answer 1

(i) sin 75°

sin(45+30)°

sin30cos45+sin45cos30

1/2×1/√2+1/√2×√3/2

1/2√2+3/2√2

1+√3/2√2

(ii) tan 15°

Clearly, tan15°=tan(45°-30°)

We know that,

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

So, tan15°=tan(45°-30°)

=(tan 45°-tan30°)/(1+tan45°.tan30°)

=[{1-(1/√3)}/{1+(1)(1/√3)}]

=(√3–1)/(√3+1)

Rationalising the denominator, we have,

Tan15°= {(√3–1)×(√3–1)}/{(√3+1)×(√3–1)}

=(3+1–2√3)/(3–1)

=(4–2√3)/2

=2-√3.

hope it helps you.....✌️