Question 5 If sin-2 cos-1- then prove that 2 sin-cos-2

Given, sin θ + 2 cos θ=1 On squaring both sides, we get; (sin θ + 2 cos θ)^2=1 ⇒ sin^2 θ + 4 cos^2 θ + 4 sin θ. cos θ =1 ⇒ (1 cos^2 θ)+4(1 sin^2 θ)+4 sin θ. ...

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Byju's Answer

Standard X

Mathematics

Complementary Trigonometric Ratios

Question 5 If...

Question

Question 5
If $s i n θ + 2 c o s θ = 1$ , then prove that $2 s i n θ - c o s θ = 2$ .

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Solution

Given, $s i n θ + 2 c o s θ = 1$

On squaring both sides, we get;

$(s i n θ + 2 c o s θ)^{2} = 1$

$\Rightarrow s i n^{2} θ + 4 c o s^{2} θ + 4 s i n θ . c o s θ = 1$

$\Rightarrow (1 - c o s^{2} θ) + 4 (1 - s i n^{2} θ) + 4 s i n θ . c o s θ = 1$

$[∵ s i n^{2} θ + c o s^{2} θ = 1]$

$\Rightarrow - c o s^{2} θ - 4 s i n^{2} θ + 4 s i n θ . c o s θ = - 4$

$\Rightarrow 4 s i n^{2} θ + c o s^{2} θ - 4 s i n θ . c o s θ = 4$

$\Rightarrow (2 s i n θ - c o s θ)^{2} = 4$

$[∵ a^{2} + b^{2} - 2 a b = (a - b)^{2}]$

$\Rightarrow 2 s i n θ - c o s θ = 2$

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Question 5 If sin θ+2 cos θ=1, then prove that 2 sin θ−cos θ=2.

Question 5
If $s i n θ + 2 c o s θ = 1$ , then prove that $2 s i n θ - c o s θ = 2$ .