Question

if cot theta =7/8 , evaluate (1+sin^2theta)(1-sin^2theta)/(1+cost^2theta)(1+co-^2theta)

the answer should be 49/64 but i couldn't get that answer. can any one help?

Answer 1

if cot theta =7/8 , evaluate (1+sin^2theta)(1-sin^2theta)/(1+cos^2theta)(1+cos-^2theta)

the answer should be 49/64 but i couldn't get that answer. can any one help?

Answer 2

if cotØ = 7/8, then tanØ = 8/7
make a sketch of the corresponding right-angled triangle to find the hypotenuse to be √113

so sinØ = 8/√113 and cosØ = 7/√113

then (1+sin^2theta)(1-sin^2theta)/(1+cos^2theta)(1+cos-^2theta)
= (1+64/113)(1-64/113)/(1+49/113)^2
= (1 - 64^2/113^2)/(162/113)^2
= (8673/113^2) / (26244/13^2)
= 8673/2644
≠ 49/64

check your typing of the expression, the end part of
cos-^2theta makes no sense