Question

cot theta + tan theta is equal to cos 6 theta into sec theta
$\cot( + \tan( = \cosec \times \sec( = ) ) ) )$
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Answer 1

If secθ+tanθ=2, then the value of sinθ is what ?

We know that:

sec²θ - tan²θ = 1

sin²θ + cos²θ = 1

By using a² - b² = (a + b)(a - b):

(sec θ + tan θ)(sec θ - tan θ) = 1

2(sec θ - tan θ) = 1

sec θ - tan θ = 1/2

Eliminating we get:

sec θ + tan θ = 2

sec θ - tan θ = 1/2

(sec θ + tan θ) + (sec θ - tan θ) = 2 + 1/2

2sec θ = 5/2

sec θ = 5/4

cos θ = 4/5

sin²θ + (4/5)² = 1

sin²θ + 16/25 = 1

sin²θ = 9/25

sin θ = ±(3/5)

Let's check which quadrant does sin θ falls to:

sec θ = 5/4 (+)

sec θ + tan θ = 2

5/4 + tan θ = 2

tan θ = 3/4 (+)

That means sin θ falls to quadrant I, meaning

sin θ = 3/5.

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