If theta and 2theta-45^circ are acute angles such that sintheta=cos(2theta-45^circ), then tantheta is equal to:

Q: If $\theta$ and $2\theta-45^\circ$ are acute angles such that $\sin\theta=\cos(2\theta-45^\circ),$ then $\tan\theta$ is equal to:

Given that: $\sin\theta=\cos(2\theta-45^\circ)$ and $\theta$ and $2\theta-45$ are acute angles We have to find $\tan\theta$ $\Rightarrow\sin\theta=\cos(2\theta-45^\circ)$ $\Rightarrow\cos(90^\circ-\theta)=\cos(2\theta-45^\circ)$ $\Rightarrow90^\circ-\theta=2\theta-45^\circ$ $\Rightarrow3\theta=135^\circ$ Where $\theta$ and $2\theta-45^\circ$ are acute angles Since $\theta=45^\circ$ Now $\tan\theta$ $=\tan45^\circ$ Put $\theta=45^\circ$ $=1$ Hence the correct option is $(a)$

M.C.Q (1 Marks)

GSEB - English Medium

If $\theta$ and $2\theta-45^\circ$ are acute angles such that $\sin\theta=\cos(2\theta-45^\circ),$ then $\tan\theta$ is equal to:

A$1$
B$-1$
C$\sqrt{3}$
D$\frac{1}{\sqrt{3}}$

STD 10
Maths
Trigonometric Ratios
R.D. Sharma

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