If 7 sin 2-3 cos 2-4- then sec -cosec- is equal to

The correct option is B 2/√(3)+2 7 sin^2θ +3 cos^2θ =4 ⇒ 7 sin^2θ + 3(1 sin^2θ) =4 ⇒ 7sin^2θ + 3 3sin^2θ = 4 ⇒ 4sin^2θ = 1 ⇒ sin^2θ = 1/4 ⇒sinθ = 1/2 ∴θ = 30 ...

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Byju's Answer

Standard X

Mathematics

Complementary Trigonometric Ratios

If 7 sin 2θ+3...

Question

If $7 s i n^{2} θ + 3 c o s^{2} θ = 4$ , then $s e c θ + c o s e c θ$ is equal to

$\frac{2}{\sqrt{3}} - 2$

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$\frac{2}{\sqrt{3}} + 2$

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$\frac{2}{\sqrt{3}}$

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None of these

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Solution

The correct option is B
$\frac{2}{\sqrt{3}} + 2$

$7 {sin}^{2} θ + 3 {cos}^{2} θ = 4 \Rightarrow 7 {sin}^{2} θ + 3 (1 - {sin}^{2} θ) = 4 \Rightarrow 7 s i n^{2} θ + 3 - 3 s i n^{2} θ = 4 \Rightarrow 4 s i n^{2} θ = 1 \Rightarrow s i n^{2} θ = \frac{1}{4} \Rightarrow sin θ = \frac{1}{2} ∴ θ = 30^{\circ} ∴ s e c 30^{\circ} + c o s e c 30^{\circ} = \frac{2}{\sqrt{3}} + 2$

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Similar questions

Q. If

7 {sin}^{2} θ + 3 {cos}^{2} θ = 4

then prove that

sec θ + cosec θ = 2 + \frac{2}{\sqrt{3}}

Q. If

3 {cos}^{2} θ + 7 {sin}^{2} θ = 4

, show that

cot θ = \sqrt{3}

Q. If

7 {sin}^{2} θ + 3 {cos}^{2} θ = 4

then find the value of

tan θ

θ

being acute.

Q. If 7 sin² θ + 3 cos²θ = 4, show that tan θ =

\frac{1}{\sqrt{3}}

If $7 s i n^{2} θ + 3 c o s^{2} θ = 4$ , then $s e c θ + c o s e c θ$ is equal to

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If 7sin2θ+3cos2θ=4, then secθ+cosecθ is equal to

The correct option is B 2√3+2 7sin2θ+3cos2θ=4⇒7sin2θ+3(1−sin2θ)=4⇒7sin2θ+3−3sin2θ=4⇒4sin2θ=1⇒sin2θ=14⇒sinθ=12∴θ=30∘∴sec30∘+cosec30∘=2√3+2

If $7 s i n^{2} θ + 3 c o s^{2} θ = 4$ , then $s e c θ + c o s e c θ$ is equal to