Question

find the value of 2 sin^2 30° - 3 cos^2 45° + tan^2 60°+ 3 sin^2 90°​

Answer 1

Step-by-step explanation:

2×(1/2)^2-3×(1/√2)^2 +(√3)^2 +3(1)^2

2×1/4 -3/2 +3+3

1-3+6+6/2 = 5

Answer 2

Solution:-

$\rm \implies2 \sin {}^{2} 30 {}^{o} - 3 \cos {}^{2} 45 {}^{o} + \tan {}^{2} 60 {}^{o} + 3 \sin {}^{2} 90 {}^{o}$

We know that the value of

$\rm \: \to \sin30 {}^{o} = \dfrac{1}{2}$

$\rm \to \cos45 {}^{o} = \dfrac{1}{ \sqrt{2} }$

$\rm \to \: \tan60 {}^{o} = \sqrt{3}$

$\rm \to \sin90 {}^{o} = 1$

Now put the value

$\rm \implies2 \sin {}^{2} 30 {}^{o} - 3 \cos {}^{2} 45 {}^{o} + \tan {}^{2} 60 {}^{o} + 3 \sin {}^{2} 90 {}^{o}$

$\rm \implies \: 2 \times \bigg(\dfrac{1}{2} \bigg) ^{2} - 3 \times \bigg(\dfrac{1}{ \sqrt{2} } \bigg) ^{2} + ( \sqrt{3} ) {}^{2} + 3 \times 1$

$\rm \: \implies \: 2 \times \dfrac{1}{4} - 3 \times \dfrac{1}{2} + 3 + 3 \times 1$

$\rm \implies \dfrac{1}{2} - \dfrac{3}{2} + 6$

$\rm \implies \: \dfrac{1 - 3 + 12}{2}$

$\rm \implies \dfrac{1 3 - 3}{2}$

$\rm \: \implies \dfrac{10}{2}$

$\rm \: 5$

Answer = 5