Question

Prove that (sinA-cosecA)(cosA-secA) = 1/(tanA+cotA)

Answer 1

heya friend11✔

Here is ur answer...
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From lhs ..

(sinA-cosecA)(cosA-secA)

=>(sinA-1/sinA)(cosA-1/cosA)

=>(sin^2A-1/sinA)*(cos^2A-1)/cosA

=>(cos^2A/sin^2A*)*(sin^2A/cosA) ...【•*•sin^2A-1=cos^2A ...and cos&2A-1=sin^2A】

=>cos^2A*sin^2A/cosA*sinA

=>cosA*sinA.......lhs...

again....from..Rhs ....

1/(tanA+cotA)

=>1/sinA/cosA+cosA/sinA

=>1/sin^2A+cos^2A/sinA*cosA.

=>1/1/sinA*cosA...【cos^2A+sin^2A=1】

so.....sinA*cosA....Rhs=lhs ....prooved...here...
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hope it help you...☺

@Rajukumar☺☺☺