Question

Sec theta ( 1 - sin theta ) (sec theta + tan theta ) = 1

Answer 1

Answer:

multiply first bracket by sec thita

Step-by-step explanation:

for more details find the attatched file

Answer 2

Complete question: Prove that $sec\theta(1-sin \theta)(sec\theta+tan\theta)=1$.

Given,

An expression: $sec\theta(1-sin \theta)(sec\theta+tan\theta)$.

To Find,

We need to prove that $sec\theta(1-sin \theta)(sec\theta+tan\theta)=1$.

Solution,

The proof of the given statement is as follows -

We need to simplify the expression.

$sec\theta(1-sin \theta)(sec\theta+tan\theta)$

$=(sec\theta-sec\theta *sin\theta)(sec\theta +tan\theta)$

$=(sec\theta - \frac{1}{cos\theta}*sin\theta } }) (sec\theta+tan\theta)$

$=(sec\theta-tan\theta)(Sec \theta+tan\theta )$ [Since $\frac{sin \theta}{cos \theta}=tan\theta$ ]

$=(sec^2\theta - tan^2\theta)=1$   [We know that $(a+b)(a-b)=(a^2-b^2)$]

Hence, the statement is proved.

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