Question

Simplify cos^2 Θ(1 + tan^2 Θ)

Answer 1

cos²Θ(1+tan²Θ) = cos²Θ + cos²Θ * tan²Θ = cos²Θ + sin²Θ ( tanΘ=sinΘ/cosΘ )
= 1

Answer 2

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

Answer 3

\[\cos ^{2}(\theta)+\sin ^{2}(\theta)=1\]
This is a trig identity

Answer 4

here are the answers:
(1) cos2 Θ + sin2 Θ
(2) cos2 Θ
(3) 1
(4) −1

Answer 5

according to the the two solutions posted by @math&ing001 and I what looks to be the correct answer?

Answer 6

(3) 1 is the correct answer
@math&ing001 is right

Answer 7

i understand the distribution os²Θ(1+tan²Θ) = cos²Θ + cos²Θ * tan²Θ
and I know that ( tanΘ=sinΘ/cosΘ )
How does this give me answer of 1?

Answer 8

you have to know the trig identity \[\sin ^{2}(\theta)+\cos ^{2}(\theta)=1\]
This is something you have to memorize

Answer 9

http://www.heykiki.com/blog/wp-content/uploads/2012/12/a.gif
here are some trig identities, that may help you understand them better

Answer 10

i know this by heart sin2(θ)+cos2(θ)=1
here is what i need to understand, how does "cos²Θ + cos²Θ * tan²Θ" equals "cos²Θ + sin²Θ"
I am not getting how the "tan²Θ" disappears
cos²Θ(1+tan²Θ) = cos²Θ + cos²Θ * tan²Θ = cos²Θ + sin²Θ = 1

Answer 11

http://www.amsi.org.au/teacher_modules/D5/D5g1.png

here is an image demonstrating the trig identity

Answer 12

\[\tan ^{2}(\theta)=\frac{ \sin ^{2}(\theta) }{ \cos ^{2}(\theta) }\]

Answer 13

multiply tan^2(x) and cos^2(x) and you are left with just sin^2(x)

Answer 14

got it :) THANK YOU ALL!