Question

If tan theta =1/root 3 , then find the value of (4 cos ^2 theta - 3)/(3 sin ^2 theta + 1) .​

Answer 1

Answer:

tan theta =1/root 3

tan theta =tan30 degree

theta = 30 degree

So,

(4 cos ^2 theta - 3)/(3 sin ^2 theta + 1)

(4 cos ^2 30degree - 3)/(3 sin ^2 30degree + 1)

(4 (root3/2)² - 3)/(3 (1/2²) + 1)

(4×3/4 - 3)/(3×1/4 + 1)

(3/4 - 3)/(3/4 + 1)

(3-12/4)/(3+4/4)

(-9/4)/(7/4)

-9/7 -----------------(Answer)