If cos 2 -a then cos 3 -cos- equals to

The correct option is B 2a 1 cos3θ/cosθ = 4cos^3 θ 3/cosθ cosθ = 4 cos^2 θ 3 = 2 (1+cos2θ) 3 = 2(1+a) 3 = 2a 1 ...

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Standard XI

Mathematics

Trigonometric Ratios of Multiples of an Angle

If cos 2 θ=a ...

Question

If $c o s 2 θ = a$ then $\frac{c o s 3 θ}{c o s θ}$ equals to

2a+1

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2a-1

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2a-2

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2a+2

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Solution

The correct option is B
2a-1

$\frac{c o s 3 θ}{c o s θ} = \frac{4 c o s^{3} θ - 3}{c o s θ} c o s θ$

= 4 $c o s^{2} θ - 3$

= 2 $(1 + c o s 2 θ) - 3$

= 2(1+a) - 3

= 2a - 1

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If cos2θ=a then cos3θcosθ equals to

The correct option is B 2a-1 cos3θcosθ=4cos3θ−3cosθcosθ = 4 cos2θ−3 = 2 (1+cos2θ)−3 = 2(1+a) - 3 = 2a - 1

If $c o s 2 θ = a$ then $\frac{c o s 3 θ}{c o s θ}$ equals to

The correct option is B
2a-1

$\frac{c o s 3 θ}{c o s θ} = \frac{4 c o s^{3} θ - 3}{c o s θ} c o s θ$

= 4 $c o s^{2} θ - 3$

= 2 $(1 + c o s 2 θ) - 3$

= 2(1+a) - 3

= 2a - 1