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(cosec A -secA )(cot A-Tan A)=(cosec …

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(cosec A -secA )(cot A-Tan A)=(cosec A+secA )(SecA cosecA -2 )
  • 1 answers

Rohit Kumar 4 years, 10 months ago

LHS:- (cosecA-secA)( cotA-tanA) => (1/sinA-1/cosA)(cosA/sinA-sinA/cosA) => (cosA-sinA/sinAcosA)(Cos^2A-sin^2A/sinAcosA) => (cosA-sinA)(cosA+sinA)(cosA-sinA) /(sinAcosA)^2 => (cosA-sinA)^2(cosA+sinA)/(sinAcosA)^2 => (cos^2A+sin^2A-2cosAsinA)(cosA+sinA)/(sinAcosA)^2 => (1-2cosAsinA)/(cosAsinA) (cosA+sinA)/(cosAsinA) (since cos^2A+sin^2A=1) => (1/cosAsinA-2cosAsinA/cosAsinA)(cosA/cosAsinA+sinA/cosAsinA) => (secAcosecA-2)(cosecA+secA) Hence, LHS=RHS
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