Question

secA - tanA cos^2A
----------------- = --------------
secA + tanA (1 + sinA)^2​

Answer 1

Answer:

secA-tanA

---------------- =LHS

secA+tanA

Step-by-step explanation:

Let secA=1/cosA

tanA=sinA/cosA

secA-tanA

----------------

secA+tanA

=(1/cosA-sinA/CosA)

-----------------------------

(1/cos A+sinA/cosA)

=(1-sinA)/cosA×cosA/(1+sinA)

=(1-sinA)

--------------

(1+sinA)

Multiplying by (1+sinA)/(1+sinA)

1-sin^2A

-------------

1+sin^2A

=cos^2A

----------------=RHS

1+sin^2A

Therefore Hence Proved

Hope it helps

Answer 2

Answer:

secA-tanA. (1/cosA)-(sinA/cosA)

......,............. =. ......................................

secA+tanA. (1/cosA)+(sinA/cosA)

= (1-sinA). 1+sinA

............. * .............

(1+sinA). 1+sinA

=1^2-sin^2 A. cos^2 A

..................... = ...................

(1+sinA)^2. (1+sinA)^2