Question

Given : 4 sin θ= 3 cos θ; find the value of :
(i) sin θ
(ii) cos θ
(iii) cot^2 θ - cosec^2 θ
(iv) 4 cos^2 θ- 3 sin^2θ+ 2​

Answer 1

Step-by-step explanation:

4 sin θ= 3 cos θ

sin θ/cos θ = 3/4

tanθ= 3/4

hyp=root(3^2+4^2)=root(9+16)=root(25)=5

i) sin θ= 3/5

ii) cos θ=4/5

iii) cot^2 θ - cosec^2 θ= -( cosec^2 θ - cot^2 θ)

= -1

iv)4 cos^2 θ- 3 sin^2θ+ 2 =4(4/5)^2 - 3(3/5)^2 +2

=64/25 - 27/25 +2

=(64-27+50)/25

= 87/25