Question

7cosec ɸ - 3cot ɸ = 7 prove that 7cot ɸ - 3cosec ɸ = 3

Answer 1

Squaring, 7cosec @ - 3cot @ = 7 throughout, we have

=> 49cosec^2 @ + 9cot^2 @ - 42cosec@cot@ = 49

=> 49(1 + cot^2 @) + 9(cosec^2 @ - 1 ) - 42cosec@cot@ = 49

=> 49 + 49 cot^2 @) + 9 cosec^2 @ - 9 - 42cosec@cot@ = 49

=> 49 cot^2 @) + 9 cosec^2 @ - 42cosec@cot@ = 9

=> (7cot @ - 3 cosec @)^2 = (3)^2

=> 7cot @ - 3 cosec @) = 3

Thus proved