Math, asked by dibashparui2020, 3 months ago

Find the value of sin^2 30 degree + cos^2 30 degree + tan^2 45 degree.
I will mark the best answer as BRAINLIEST.

Answers

Answered by ritika123489
0

Step-by-step explanation:

this is your answer in image

Attachments:
Answered by rekharajput0919
0

Answer:

In this question, we need to evaluate the following expression i.e.

\dfrac{5\sin^230+\cos^245-4\tan^2 30}{2\sin30\cos30+\tan45}

2sin30cos30+tan45

5sin

2

30+cos

2

45−4tan

2

30

The values of following trigonometric quantities are:

\begin{gathered}\sin30=\dfrac{1}{2}\\\\\cos45=\dfrac{1}{\sqrt2}\\\\\tan 30=\dfrac{1}{\sqrt 3}\\\\\cos30=\dfrac{\sqrt3}{2}\\\\\tan45=1\end{gathered}

sin30=

2

1

cos45=

2

1

tan30=

3

1

cos30=

2

3

tan45=1

So,

\begin{gathered}=\dfrac{5\times (\dfrac{1}{2})^2+(\dfrac{1}{\sqrt2})^2-4\times (\dfrac{1}{\sqrt3})^2}{2\times \dfrac{1}{2}\times \dfrac{\sqrt3}{2}+1}\\\\=\dfrac{\dfrac{5}{4}+\dfrac{1}{2}-\dfrac{4}{3}}{\dfrac{\sqrt3}{2}+1}\\\\=\dfrac{5}{6(\sqrt 3+2)}\end{gathered}

=

2

1

×

2

3

+1

5×(

2

1

)

2

+(

2

1

)

2

−4×(

3

1

)

2

=

2

3

+1

4

5

+

2

1

3

4

=

6(

3

+2)

5

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