CBSE BOARD XII, asked by jessiemonias5229, 1 year ago

Sin inverse 3/5+tan inverse 3/4

Answers

Answered by mayuresh18
0

Answer:

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Explanation:

2sin

−1

5

3

−tan

−1

31

17

=

4

as we know triangle triplet is (3,4,5). so we use this in our proving at the time use.

now we have to prove L.H.S =R.H.S

\begin{lgathered}2\sin^{-1}\frac{3}{5}-\tan^{-1}\frac{17}{31}=\frac{\prod }{4}\\\\2\tan^{-1}\frac{3}{4}-\tan^{-1}\frac{17}{31}=\frac{\prod }{4}\\\\\tan^{-1}\frac{2*\frac{3}{4}}{1-(\frac{3}{4})^{2}}-\tan^{-1}\frac{17}{31}=\frac{\prod }{4}\\\\\tan^{-1}\frac{24}{7}-\tan^{-1}\frac{17}{31}=\frac{\prod }{4}\\\\\tan^{-1}\frac{\frac{24}{7}-\frac{17}{31}}{1+\frac{24}{7}*\frac{17}{31}}=\frac{\prod }{4}\\\\\tan^{-1}(1)=\frac{\prod }{4}\\\\\frac{\prod }{4}=\frac{\prod }{4}\end{lgathered}

2sin

−1

5

3

−tan

−1

31

17

=

4

2tan

−1

4

3

−tan

−1

31

17

=

4

tan

−1

1−(

4

3

)

2

2∗

4

3

−tan

−1

31

17

=

4

tan

−1

7

24

−tan

−1

31

17

=

4

tan

−1

1+

7

24

31

17

7

24

31

17

=

4

tan

−1

(1)=

4

4

=

4

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