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(1-cos A)(1+sec A)=tan A sin A. Please answer this question faster

(1-cos A)(1+sec A)=tan A sin A. Please answer this question faster

Grade:10

1 Answers

Sujit Kumar
111 Points
3 years ago
I am assuming the question is : Prove that SinATanA=(1-CosA)(1+SecA)
 
(1-CosA)(1+SecA)=TanASinA
Transposing \ (1-CosA) \ to \ RHS
=>(TanA)(SinA)(\frac{1}{1-CosA})=(1+SecA)__________(1)
Taking only the LHS from equation (1)
=>(\frac{SinA}{CosA})(SinA)(\frac{1}{1-CosA})
=>(Sin^2A)(\frac{1}{CosA-Cos^2A})
=>\frac{Sin^2A}{CosA-Cos^2A}
(Note: \ Sin^2x=1-Cos^2x)
=>\frac{1-Cos^2A}{CosA-Cos^2A}
(Note: \ a^2-b^2=(a+b)(a-b))
=>\frac{(1+CosA)(1-CosA)}{CosA(1-CosA)}
=>\frac{(1+CosA)}{CosA}
=>\frac{1}{CosA}+1
=>SecA+1=RHS \ of \ equation \ (1)
Hence \ Proved \ !

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