Question

If 4sin theta=3, find the value of x if root cosec^2 theta-cot^2 theta/sec^2 theta-1+2cot theta=root7/x+cos theta

Answer 1

4sinθ=3
or, sinθ=3/4
∴, cosecθ=1/sinθ=4/3
∵, cosec²θ-cot²θ=1
or, cot²θ=cosec²θ-1
or, cot²θ=(4/3)²-1
or, cot²θ=16/9-1
or, cot²θ=7/9
or, cotθ=√7/3
Again, tanθ=1/cotθ=3/√7
∵, sec²θ-tan²θ=1
or, sec²θ=1+tan²θ
or, sec²θ=1+9/7
or, sec²θ=16/7
or, secθ=4/√7
∴, cosθ=1/secθ=√7/4
√(cosec²θ-cot²θ)/(sec²θ-1) + 2cotθ=√7/x + cosθ
or, √[1/{(4/√7)²-1}]+2×√7/3=√7/x+√7/4
or, √{1/(16/7-1)}+2√7/3=√7/x+√7/4
or, √1/(9/7)+2√7/3=√7/x+√7/4
or, √7/3+2√7/3=√7/x+√7/4
or, 1/3+2/3=1/x+1/4
or, -1/x=1/4-1/3-2/3
or, -1/x=1/4-(1/3+2/3)
or, -1/x=1/4-1
or, -1/x=-3/4
or, x=4/3 Ans.

Answer 2

hope it helps......enjoy...