Question

If 7cosecθ - 3cotθ = 7, find 7cotθ - 3cosecθ

Answer 1

7 cosecθ - 3cotθ = 7

squaring both the side

( 7 cosecθ - 3cotθ )^2 = 7^2

using (a - b)^2 = a^2 + b^2 - 2ab

49cosec^2 θ + 9 cot^2 θ - 2×(7cosecθ)(3cotθ)= 49

using cosec^2 θ = 1 + cot^2 θ

using cot ^2 θ= cosec^2 θ - 1

49(1+ cot^2 θ) + 9(cosec^2 θ - 1) - 42cosecθcotθ = 49

49 + 49cot^2 θ + 9cosec^2θ - 9 - 42cosecθcotθ = 49

( 7cotθ)^2 +(3cosecθ )^2 - 2×(7cosecθ)(3cotθ) = 9

(7cot θ - 3cosec θ)^2 = 3^2

7cot θ - 3cosec θ= 3

7cot θ - 3cosec θ= 3

also see the attachment