Trigonometric Functions - Maharashtra Board STD 12 Science Maths Questions

In $\triangle ABC$ with usual notations, prove that : $2\left\{a \sin ^2\left(\frac{ C }{2}\right)+c \sin ^2\left(\frac{ A }{2}\right)\right\}=(a+c-b)$

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Q 12Solve the Following Question.(3 Marks)3 Marks

Show that : $2 \sin ^{-1}\left(\frac{3}{5}\right)=\tan ^{-1}\left(\frac{24}{7}\right)$

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Q 13Solve the Following Question.(3 Marks)3 Marks

If $2 \tan ^{-1}(\cos x)=\tan ^{-1}(2 \operatorname{cosec} x)$, then find the value of $x$.

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Q 14Solve the Following Question.(3 Marks)3 Marks

Show that : $\sin ^{-1}\left(\frac{8}{17}\right)+\sin ^{-1}\left(\frac{3}{5}\right)=\sin ^{-1}\left(\frac{77}{85}\right)$

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Q 15Solve the Following Question.(4 Marks)4 Marks

In $\triangle A B C$ with usual notations, prove that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}=2 R$ where $R$ is the circumradius of $\triangle ABC$.

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Q 16Solve the Following Question.(4 Marks)4 Marks

If $\tan ^{-1}\left(\frac{x-1}{x-2}\right)+\cot ^{-1}\left(\frac{x+2}{x+1}\right)=\frac{\pi}{4}$; find $x$.

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Q 17Solve the Following Question.(4 Marks)4 Marks

Show that the angle between any two diagonals of a cube is $\cos ^{-1}\left(\frac{1}{3}\right)$

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Q 18Solve the Following Question.(4 Marks)4 Marks

In $\triangle ABC$, prove that : $\tan \frac{( A - B )}{2}=\left(\frac{a-b}{a+b}\right) \cdot \cot \frac{ C }{2}$

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Q 19Solve the Following Question.(4 Marks)4 Marks

Find the general solution of : $\sin x \tan x=\tan x-\sin x+1$.