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(tanA/1-cotA) +(cotA/1-tanA)=1+secAcosecA

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(tanA/1-cotA) +(cotA/1-tanA)=1+secAcosecA

Posted by H Bansal 5 years, 10 months ago

CBSE > Class 10 > Mathematics

2 answers

Aadya Singh 5 years, 10 months ago

LHS - (tanA / 1-cot A) + (cot A /1 - tan A)
=> [sinA/cosA/(1- cosA/sinA)] + [cosA/sinA/(1- sinA/cosA ]
=> [ sinA / cosA / sinA-cosA/sinA] + [ cosA/sinA/cosA-sinA/cosA]
=>[ sin²A / cosA(sinA - cosA)] + [ cos²A/sinA(cosA - sinA) ]
=> [ sin²A/cosA(sinA - cosA) ] - [ cos²A/sinA ( sinA - cosA)]
=> [( sin³ A - cos³A)/ sinAcosA(sinA - cosA)
=> (sinA - cosA)( sin²A + cos²A + sinAcosA) / sinAcosA(sinA - cosA)
=> (sin²A + cos²A + sinAcosA) / sinAcosA
=> ( 1 + sinAcosA)/ sinAcosA
=> 1/sinAcosA + 1
=> cosecA secA + 1
=> secAcosecA + 1
=> Now, LHS = RHS....So, it's prove...

2Thank You

H Bansal 5 years, 10 months ago

Pls answer fast ??

6Thank You

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