Question

If 6 sin theta + 7 cos theta =9 , then tan theta ?
Then find the value of 7cos theta -6 sin theta

Answer 1

Answer:

given

6 sin theta + 7 cos theta =9(equation 1)

let us assume

7 cos theta - 6 sin theta=k(equation 2)

0

squaring and adding on both sides of equation 1 and 2

(6 sin theta+7 cos theta)^2+ (7 cos theta _ 6 sin theta)^2=9^2+k^2

36 sin^2theta+9 cos square theta + 84 sin theta cos theta + 49 sin ^2 theta + 36 cos^2theta -86 sin theta cos theta=81+k^2

85 sin^2theta + 85 cos^2 theta is equals to 81 + k ^2

85(sin^2 theta + cos^2theta)=81+k^2

85(1)=81+k^2

85=81-k^2

85-81=k^2

4=k^2

2=k

4=k