Question

cos^2 theta (1+tan^2 theta)

Answer 1

\[\cos ^{2}\theta (1+\tan ^{2}\theta)\]

Answer 2

Hint: \(\tan(x)=\frac{\sin(x)}{\cos(x)}\)

\(a(b+c)=ab+ac\)

\(a\frac{a}{b}=b\)

\(\cos^2(x)+\sin^2(x)=1\)

Answer 3

i got the answer 1

Answer 4

am i right ?

Answer 5

yep

Answer 6

I am not sure how strict your teacher is, but \(1\) as a function does not have a restricted domain, where the function on the left side does, so you may need to say something like \(..=1\) as long as \(\theta \ne \) something that makes cosine \(0\).

Answer 7

\[\cos^2 \theta \left( 1+\tan ^2\theta \right)=\cos ^2\theta \sec ^2\theta=\frac{ \cos ^2\theta }{ \cos ^2\theta }=1\]
if\[\cos \theta \neq 0\]

Answer 8

This is another way \(\uparrow\)

Using the fact that if we divide \(\cos^2(x)+\sin^2(x)=1\) on both sides by \(\cos^2(x)\) we get \(1+\tan^2(x)=\sec^2(x)\)