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Question 1

Question 2

Answer:

Identity is true

Explanation:

$(cos\theta+1)/(tan^2\theta)=(cos\theta)/(sec\theta-1)$

$(cos\theta+1)(sec\theta-1)=(tan^2\theta)(cos\theta)$

$(cos\theta)(sec\theta)+(cos\theta)(-1)+(1)(sec\theta)+(1)(-1)=((sin^2\theta)/(cos^2\theta))(cos\theta)$

$(cos\theta)((1)/(cos\theta))-cos\theta+sec\theta-1=(sin^2\theta)/(cos\theta)$

$1-cos\theta+sec\theta-1=(sin^2\theta)/(cos\theta)$

$-cos\theta+sec\theta=(sin^2\theta)/(cos\theta)$

$sec\theta-cos\theta=(sin^2\theta)/(cos\theta)$

$(1)/(cos\theta)-cos\theta=(sin^2\theta)/(cos\theta)$

$(1)/(cos\theta)-(cos^2\theta)/(cos\theta)=(sin^2\theta)/(cos\theta)$

$(1-cos^2\theta)/(cos\theta)=(sin^2\theta)/(cos\theta)$

$(sin^2\theta)/(cos\theta)=(sin^2\theta)/(cos\theta)$

Therefore, the identity is true.

Helpful tips:

Pythagorean Identity:
$sin^2\theta+cos^2\theta=1\\cos^2\theta=1-sin^2\theta\\sin^2\theta=1-cos^2\theta$

Quotient Identities:
$tan\theta=(sin\theta)/(cos\theta),sec\theta=(1)/(cos\theta)$

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