Question

tan(π\4+a) / tan(π\4-a) = 1+sin2a / 1-sin2a​

Answer 1

Answer:

Step-by-step explanation:

tan(π\4+a) / tan(π\4-a) = 1+sin2a / 1-sin2a​

By taking Lhs:

tan(π\4+a) / tan(π\4-a)

now expand the numerator and denominator using the frmla:

tan(x±y) = tanx ±tany/1± tanx.tany

by simplifying:

(1+tanA)²/(1-tanA)²

= (1 + tan²a + 2tanA)/(1 + tan²a - 2tanA)

now we no that 1 + tan²A= sec²a  soooo

and sec²a = 1/ cos²a

∴ 1/cos²a + 2.sinA/cosA÷ 1/cos²a - 2.sinA/cosA

∴1+sin2A/1-sin2A

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HENCE PROVED

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