Question

prove that (secA-cosecA) (1+tanA+cotA)=tanA secA - cotA cosec A​

Answer 1

Step-by-step explanation:

LHS=(secA-cosecA) ( 1+tan A+cotA)

( 1/cos A- 1/sinA) ( 1+sinA/cosA+cosA/sinA)

sinA-cosA/sinA.cosA ( cosA.sinA+sinA.cosA/cosA.sinA)

sinA-cosA/sinA.cosA( cosA.sinA+sin^A +cos^A/cos.sinA)

=sinA-cosA/sinA.cosA( cosA.sinA+1/cosA.sinaA)

=(sinA-cosA) ( cisA.sinA+1)/sin^A cos^A

=sin^A.cos^A-cos^A.sinA-cosA/sin^A.cos^A

=(sin^A.cosA-cosA)+( sinA-cos^A.sinA)/sin^A.cos^A

=cosA( sin^A-1)+sinA(1-cos^A)/cos^A.cos^A

=cosA(-cos^A)+sinA(sin^A)/sin^A.cos^A

=-cos cubeA+sin cube A/sin^A.cos^A

=sin cubeA-cos cubeA/sin^A.cos^A

=sin cubeA/sin^A.cos^A-cos cube A/sin^A.cos^A

= sinA/cos^A-cosA/sin^A

tanA.secA-cotA.cosecA RHS