Question

Show that cos(1/1-sin-(1/1+sin)can be written in the form of K tan. And find the value of k.

Answer 1

The expression cos(1/1-sin-(1/1+sin)) can be written in the form of K tan, where K = 1/√(1 + sin^2(x)).

Step-by-step explanation:

To show that cos(1/1-sin-(1/1+sin)) can be written in the form of K tan, we can start by expressing sin(1/1-sin-(1/1+sin)) in terms of tan by using the identity sin(x) = tan(x)/√(1 + tan^2(x)).

Letting x = 1/1-sin-(1/1+sin), we have sin(x) = tan(x)/√(1 + tan^2(x)).

Substituting this back into the original expression, we have cos(1/1-sin-(1/1+sin)) = cos(x) = 1/√(1 + tan^2(x)) = 1/√(1 + (sin(x)/√(1 + tan^2(x)))^2).

This can be further simplified to cos(1/1-sin-(1/1+sin)) = 1/√(1 + sin^2(x)).

So, we can write cos(1/1-sin-(1/1+sin)) as K tan(x) by choosing K = 1/√(1 + sin^2(x)).

Therefore, the value of K is 1/√(1 + sin^2(x)).