Question

The value of 2(sin ^4 30°+ cos ^4 60°) - (tan^2 60°+ cot^2 45°) + 3cosec²60° is​

Answer 1

EXPLANATION.

Evaluate :

⇒ 2(sin⁴30° + cos⁴60°) - (tan²60° + cot²45°) + 3cosec²60°.

As we know that,

Formula of :

⇒ sin30° = 1/2.

⇒ cos60° = 1/2.

⇒ tan60° = √3.

⇒ cot45° = 1.

cosec60° = 2/√3.

Using this formula in the equation, we get.

⇒ 2[(1/2)⁴ + (1/2)⁴] - [(√3)² + (1)²] + 3(2/√3)².

⇒ 2[1/16 + 1/16] - [3 + 1] + 3[4/3].

⇒ 2[2/16] - [4] + [4].

⇒ [4/16] - [4] + [4].

⇒ 1/4 - 4 + 4.

⇒ 1/4.

Answer 2

given★

• 2(sin ^4 30°+ cos ^4 60°) - (tan^2 60°+ cot^2 45°) + 3cosec²60°

solution

• $\star\purple{2(sin ^4 30°+ cos ^4 60°) - (tan^2 60°+ cot^2 45°) + 3cosec²60°}$ --------(1)

• we know that value of

• $\sin(30) = \frac{1}{2} \\ \\ \cos(60) = \frac{1}{2} \\ \\ \tan(60) = \sqrt{3} \\ \\ \cot(45 ) = 1 \\ \\ \cosec(30) = \frac{2}{ \sqrt{3} }$
• ------------(2)

question according

• eq(2) value put on eq (1)

• $2( (\frac{1}{2}) {}^{4} +( \frac{1}{2} ) {}^{4} ) - (( \sqrt{3}) {}^{2} + 1 {}^{2} ) + 3( \frac{2}{ \sqrt{3} }) {}^{2}$

• $2( \frac{1}{16} + \frac{1}{16} ) - (3 + 1) + 3 \times \frac{4}{3}$

• $2( \frac{2}{16}) - 4 + 4$

• $2 \times \frac{1}{8}$

• $\frac{1}{4}$

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answer

• 1/4

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I hope it helps you