Question

Heya Friends...

A question from trigonometry according to class 10 CBSE...

Prove that -

sin²A tan A + cos²A cot A + 2 sin A × cos A = tan A + cot A

Plz give the answer with clear steps.....

Answer 1

HELLO DEAR,


I HOPE ITS HELP YOU DEAR,

THANKS

Answer 2

Heya bhai kraish ...✔

Here is your answer....
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From lhs....

sin^2A*tanA+cos^2A*cotA+2sinA*cosA

=>sin^2A*sinA/cosA+cos^2A*cosA*/sinA+2sinA*cosA


=>sin^3A/cosA+cos^3A/sinA+2cosA*sinA

=>sin^4A+cos^4A+2sin^2A*cos^2A/sinA*cosA/sinA*cosA


【lcm here ....】

=>sin^4A+cos^4A+2sin^2A*cos^2A/sinA*cosA

=>【(sin^4+cos^4A)+(2sin^2A*cos^2A)】/sinA*cosA

➡using this formula ...
(a^4+b^4)=(a^2+b^2)^2-2a^2b^2....

=>(sin^2A+cos^2A)-2sinA*cosB/sinA*cosA...

=>1-2sin^2A*cos^2A+2sin^2A*cos^2A/cosA*cosA

=>1/sinA*cosA....=cosecA*secA.....lhs...1)


now....from Rhs ...
.tanA+cotA

=>sinA/cosA+cosA/sinA

=>sin^2A+xos^2A/sinA*cosA


=>1/sinA*cosA

=>cosecA*secA.....

now ...from lhs =Rhs .......prooved ...

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hope it help you...

@Rajukumar☺☺☺