If tanA =
√2 - 1, where A is an acute angle then the value of sinA.cosA will be
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sinA.cosA = √2/4 if tanA = √2 - 1 & A is acute angle
Step-by-step explanation:
sinA.cosA
= CosATanACosA
= Cos²A. TanA
= TanA/Sec²A
= TanA / (1 + Tan²A)
= (√2 - 1 ) / ( 1 + (√2 - 1)²)
= (√2 - 1 ) / ( 1 + 2 + 1 - 2√2)
= (√2 - 1 ) / ( 4 - 2√2)
= (√2 - 1 ) / 2√2( √2 - 1)
= 1/2√2
= √2/4
sinA.cosA = √2/4
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