Question

2 sin ^2 30 - 3 cos^2 45 + tan^2 60

Answer 1

Hey Friend ☺

☆ TRIGONOMETRY ☆

sin 30 = 1/2

cos 45 = 1/root 2

tan 60 = root3

2 sin^2 30 - 3 cos^2 45 + tan ^2 60

= 2 ( 1/2 )^2 - 3 ( 1/root2 )^2 + ( root3 )^2

= 2 × 1/4 - 3 × 1/2 + 3

= 1/2 - 3/2 + 3

= - 2/2 + 3

= - 1 + 3

= 2

So 2sin^2 30 - 3cos^2 45 + tan^2 60 = 2

Hope it helps you ..!!

✌

Answer 2

Concept :

The type of mathematics deals with the relationship between the sides and angles of triangles.

Given :

We have given expression $2 sin ^2 30\textdegree - 3 cos^2 45\textdegree + tan^2 60\textdegree$.

Solution :

Now,

We know that,

$sin 30 \textdegree=\frac{1}{2}$

$cos 45\textdegree=\frac{1}{\sqrt{2} }$

$tan 60\textdegree = \sqrt{3}$

the expression is

$2 sin ^2 30\textdegree - 3 cos^2 45\textdegree + tan^2 60\textdegree$

Now, putting the values of $sin 30\textdegree , cos 45 \textdegree$ , and $tan 60 \textdegree$.

solve the expression as:

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

So, the expression $2 sin ^2 30\textdegree - 3 cos^2 45\textdegree + tan^2 60\textdegree$ answer is $2$.

Hence, the correct answer is $2$.

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