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Grade 10Trigonometry

Prove the following (1+CotA+tanA) . (sina- cosa)= secA/cosec^2A - cosec A/sec^2 A

Profile image of Jaideep markam
9 Years agoGrade 10
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1 Answer

Profile image of aditya
9 Years ago
DEAR STUDENT OR SIR 
THE SOULUTION IS 
      take LHS
   (1+cotA+tanA)(sinA-cosA)= (1+cosA/sinA+sinA/cosA)(sinA-cosA)
                                         = (sinAcosA+sin^2A+cos^2A / sinAcosA)(sinA-cosA)
                                         = (sinAcosA+1 /sinAcosA )(sinA-cosA)
                                         =cosecAsecA(sinAcosA+1)(sinA-cosA) 
                                         =cosecAsecA(sin^2acosA+sinA-sinAcos^2A-cosA)
                                         =cosecAsecA(cosA{sin^2A-1)-sinA{cos^2A-1})
                                         =cosecAsecA(cos^3A-sin^3A)
                                         =cosecAsecA(1/sec^3A-1/cosec^3A)
multipty   cosecAsecA inside we get 
                                         =secA/cosec^2A-cosecA/sec^2a 

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