Question

cos²45⁰+sin²30. Find the value of​

Answer 1

$\huge\mathbb{ANSWER:}$

Given :

• cos²45°+sin²30°

To find :

• Value of above trigonometric expression

Solution :

→cos²45°+sin²30°

As we know

• cos 45°=$\frac{1}{\sqrt{2}}$

• sin 30°=$\frac{1}{2}$

$→ \bigg(\frac{1}{ \sqrt{2} } \bigg) {}^{2} + \bigg(\frac{1}{ {2} } \bigg) {}^{2}$

$→ \frac{1}{2} + \frac{1}{4}$

• Taking LCM

$→ \frac{2 + 1}{4}$

$→ \frac{3}{4}$

$\boxed{\bf \red{ \cos {}^{2} (45 \degree) + \sin {}^{2} (30 \degree) = \frac{3}{4} }}$

Answer 2

• $\sf\fbox\red{Appropriate Question}$

cos²45°+sin²30°, Find the values of it

• $\sf\fbox\red{Given}$

cos²45⁰+sin²30

• $\sf\fbox\red{To Find}$

Value of above trigonometric expression

• $\sf\fbox\red{Solution}$

As per the question,

We have been provided the equation cos²45°+sin²30°.

As we know that according to trigonometric identity, the value of

cos45° =$\frac{1}{\sqrt{2}}$

sin30° = 0.5

Now,

On putting these value in equation cos²45°+sin²30° and further solving, we get,

cos²45°+sin²30°

$= (\frac{1}{\sqrt{2}})^{2} + (0.5)^{2}$

$= \frac{1}{2} + 0.25$

= 0.5 + 0.25

= 0.75

Hence, the required value = 0.75.