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?

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

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?

Sure! To evaluate the expression (1+sin^2(theta))(1-sin^2(theta))/(1+cos^2(theta))(1+cot^2(theta)), we need to use trigonometric identities and algebraic simplification.

Let's break it down step-by-step:

1. Start by substituting the given value cot(theta) = 7/8 into the expression:
(1+sin^2(theta))(1-sin^2(theta))/(1+cos^2(theta))(1+(7/8)^2)

2. Next, we simplify the expression by using the Pythagorean identity sin^2(theta) + cos^2(theta) = 1:
(1+sin^2(theta))(1-sin^2(theta))/(1+cos^2(theta))(1+49/64)

3. Notice that the terms (1+sin^2(theta))(1-sin^2(theta)) and (1+cos^2(theta)) cancel each other out. Using the Pythagorean identity again, we're left with:
1/(1+49/64)

4. Simplify the expression by finding a common denominator:
1/(64/64 + 49/64) = 1/(113/64)

5. To divide by a fraction, we multiply by its reciprocal:
1 * (64/113) = 64/113

Hence, the simplified expression is 64/113, not 49/64. Please double-check your calculations or provide additional context if you believe there is an error.