Question

Hey frnds !! Prove it step by step..
Ques. 8 and 11

Answer 1

Hey!!!

Good Afternoon

Note : I'll use shorter methods (from RD)

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Let's prove

Q8. To Prove

=> secA - tanA = 1/(secA + tanA) = (1 - sinA)/cosA

LHS = secA - tanA

We know sec²A - tan²A = 1

=> (secA - tanA)(secA + tanA) = 1

Sending secA + tanA on other side

=> secA - tanA = 1/secA + tanA

Easy ?

Now RHS = (1 - sinA)/cosA

=> 1/cosA - sinA/cosA

=> secA - tanA

=> LHS

Hence Proved

Easy ?

Now

Q 11. let A = a (using Brainly feature)

$\sqrt{ \frac{1 + \sin(a) }{1 - \sin(a) } } = \sec(a) + \tan(a)$

LHS =

$\sqrt{ \frac{1 + \sin(a) }{1 - \sin(a) } }$

Now multiply and divide by 1 + sin(a)

$\sqrt{ \frac{( {1 + \sin(a) })^{2} }{1 - { \sin(a) }^{2} } }$

=> We know 1 - sin²A = cos²A

Thus

=> (1 + sinA)/cosA

=> 1/cosA + sinA/cosA

=> secA + tanA

=> RHS

Hence Proved

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Hope this helps ✌️

Have a good day ahead