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.....
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.....
Add an Answer
More Questions From This User See All
Answers & Comments
I HOPE ITS HELP YOU DEAR,
THANKS
Here is your answer....
===================
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 ...
==========
hope it help you...
@Rajukumar☺☺☺