Question

If in AABC, ZC = 90°, prove that :
1-sin A
= sec A - cot B.
1 + cos B​

Answer 1

Step-by-step explanation:

A+B=90°

sinA=cosB.

=√1-sinA×(1-cosB)

______________

1+cosB×(1-cosB)

=√1-sinA-cosB+sinAcosB

____________________

√1-cos^2B

=√1-2cosB+cos^2B

______________

√sin^2B

= √(1-cosB)^2

__________

sinB

=1-cosB

______

cosA

R.H.S

=1/cosA-cosB/SinB

=cosA-cosBcosA

(cosA)(cosA)

=cosA(1-cosB)

___________

(cosA)(cosA)

=1-cosB

cosA

L.H.S=R.H.S