If 0 < θ < 90, θ, sinθ = cos30, then obtain the value of 2tan2θ — 1.

Q7 of 104 Page 196

If 0 < θ < 90, θ, sinθ = cos30, then obtain the value of 2tan²θ — 1.

cos(90–θ ) = sinθ

tan(90–θ ) = cotθ

sin(90–θ ) = cosθ

cot(90–θ ) = tanθ

cosec(90–θ ) = secθ

sec(90–θ) = cosecθ

sinθ = cos30

⇒ θ = 60

Now, 2tan²θ – 1

= 2tan²60 – 1

= 2(√3)² – 1

= 5

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If tanA = cotB, prove that A + B = 90, where A and B are measures of acute angles.

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