Question

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

Answer 1

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 2

Answer:

LHS=RHS

Step-by-step explanation:

LHS = cot a - tan a

= (cos a/sin a) -(sin a/cos a)

=(cos ^2 a - sin ^2 a)/(sin a cos a)

= (cos^2 a - 1+ cos^2 a)/(sin a cos a)

= (2 cos ^2 a - 1)/ sin a cos = RHS (proved)