Question

Prove that (2 + 2sec theta)(1 - sec theta)/(2 + 2cosec theta)(1 - cosec theta) = tan^4 theta

Answer 1

Answer:

your answer attached in the photo

Answer 2

Concept introduction:

Trigonometry is a discipline of mathematics that deals with certain angles' functions and how to use them in computations. In trigonometry, there are six functions of an angle that are often utilized. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their names and acronyms (csc).

Given:

Here the equation is $(2 + 2sec$θ$)$$(1 - sec$θ$)/$$(2 + 2cosec$θ$)$$(1 - cosec$θ$)$

To find:

We have to prove that the given equation is similar or not of $tan^4$θ.

Solution:

According to the question,

$(2 + 2sec$θ$)$$(1 - sec$θ$)/$$(2 + 2cosec$θ$)$$(1 - cosec$$)$

$=2*(1-sec^2$θ$)$$/2(1-cosec^2$θ$)$

$=-tan^2$θ$/-cot^2$θ

$=tan^4$θ

Final answer:

Hence, it is proved that the equation is same as $=tan^4$θ.

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