Question

Answer this question ASAP !!​

Answer 1

Hey Buddy

Here's The Answer

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We know , we can write

sec ø = 1/cos ø

Now

To Prove

(sec ø - 1)/(sec ø + 1) = [sin ø/1 + cos ø]^2

taking LHS

Using above Identity

(1/cos ø -1 ) / (1/cos ø + 1 )

Taking LCM

[(1 - cos ø)/cos ø]/ [(1 + cos ø)/cos ø]

(1 - cos ø)/(1 + cos ø)___(1)

By rationalising (1)

[(1 - cos ø)/(1 + cos ø)]×[((1 + cos ø)/(1 + cos ø)]

Now

(1-cos ø) × (1 + cos ø )

using identity a^2 - b^2 = (a-b)(a+b)

1 - cos^2 ø

sin^2 ø

Now solving lower part

(1 + cos ø)(1 + cos ø)

(1 + cos ø)^2

writing together

(sin^2 ø)/ (1 + cos ø)^2

now

[sin ø/1 + cos ø]^2

Hence Proved

Hope Helped

Peace ;)