Prove that:-cotA - tanA= 2cos^2 A- 1÷ sinA cosA

1.	Prove that:-cotA - tanA= 2cos^2 A- 1÷ sinA cosA
Answer» Step-by-step explanation: before i solve you must know that cotA=cosA/sinA and TANA=sina/cosA hence cotA - tanA= cosA/sinA - sinA/cosA taking LCM =cos^ 2 A - sin^2 A/sinAcosA but sin^2 A + cos^2 A=1 which implies than sin^2 A = 1 - cos^2 A putting this value in ORIGINAL EQUATION we get, cotA - tanA = cos^2 A -1 + cos^2 A/sinAcosA = 2cos^2A - 1/sinAcosA as required I hope this helps!!

Answer»

Step-by-step explanation:

before i solve you must know that cotA=cosA/sinA

and TANA=sina/cosA

hence cotA - tanA= cosA/sinA - sinA/cosA

taking LCM

=cos^ 2 A - sin^2 A/sinAcosA

but sin^2 A + cos^2 A=1

which implies than sin^2 A = 1 - cos^2 A

putting this value in ORIGINAL EQUATION

we get, cotA - tanA = cos^2 A -1 + cos^2 A/sinAcosA

= 2cos^2A - 1/sinAcosA as required

I hope this helps!!

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Prove that:-cotA - tanA= 2cos^2 A- 1÷ sinA cosA​

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Prove that:-cotA - tanA= 2cos^2 A- 1÷ sinA cosA