Write $\left( \cos ^ { 2 } x \right) \left( 1 + \tan ^ { 2 } x \right)$ in terms of $\sin x$
And $\cos x$
Then simplify
A) $1$
B) $\sin ^ { 2 } x$
C) $\sin x$
D) $\cos x$
E) $- \cos ^ { 2 } x$

Question

Quizplus · Accepted Answer

Using the trigonometric identity $1 + \tan^2x = \sec^2x$ and knowing that $\sec x = \frac{1}{\cos x}$, we can rewrite the expression as $\cos^2x \cdot \sec^2x$. Simplifying this gives $1$, since $\cos^2x \cdot \sec^2x = \cos^2x \cdot \frac{1}{\cos^2x} = 1$.

Write (cos⁡2x)(1+tan⁡2x)\left( \cos ^ { 2 } x \right) \left( 1 + \tan ^ { 2 } x \right)(cos2x)(1+tan2x)

Write $\left( \cos ^ { 2 } x \right) \left( 1 + \tan ^ { 2 } x \right)$