Question

if tan a is equal to root 2 minus 1 show that Sin A cos A is equal to root 2 by 4​

Answer 1

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If tan A = √2 - 1 , show that sin A cos A = √2/4

TanA=√2-1
or, tanA=(√2-1)(√2+1)/(√2+1)
or, tanA=(2-1)/(√2-1)
or, tanA=1/√2-1
∴, tanA+1/tanA=1/√2-1+√2-1
or, (tan²A+1)/tanA=[1+(√2-1)²]/(√2-1)
or, sec²A/tanA=(1+2-2√2+1)/(√2-1)
or, (1/cos²A)/(sinA/cosA)=(4-2√2)/(√2-1)
or, 1/sinAcosA=(4-2√2)(√2+1)/(√2-1)(√2+1)
or, 1/sinAcosA=(4√2-4+4-2√2)/(2-1)
or, 1/sinAcosA=2√2
or, sinAcosA=1/2√2
or, sinAcosA=√2/2√2.√2
or, sinAcosA=√2/4 (Proved)




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