Question
If $2\sin^2\theta-\cos^2\theta=2,$ then find the value of $\theta$.
✓
Answer
Given, $2\sin^2\theta-\cos^2\theta=2$
$\Rightarrow\ 2\sin^2\theta-(1-\sin^2\theta)=2 \ \big[\because\ \sin^2\theta+\cos^2\theta=1\big]$
$\Rightarrow\ \sin^2\theta+\sin^2\theta-1=2$
$\Rightarrow\ 3\sin^2\theta=3$
$\Rightarrow\ \sin^2\theta=1\ \big[\because\ \sin90^\circ=1\big]$
$\Rightarrow\ \sin\theta=1=\sin90^\circ$
$\therefore\ \theta=90^\circ$
$\Rightarrow\ 2\sin^2\theta-(1-\sin^2\theta)=2 \ \big[\because\ \sin^2\theta+\cos^2\theta=1\big]$
$\Rightarrow\ \sin^2\theta+\sin^2\theta-1=2$
$\Rightarrow\ 3\sin^2\theta=3$
$\Rightarrow\ \sin^2\theta=1\ \big[\because\ \sin90^\circ=1\big]$
$\Rightarrow\ \sin\theta=1=\sin90^\circ$
$\therefore\ \theta=90^\circ$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Basketball players John, Vasim, Akash were practising the ball drop in the basket. The probabilities of success for John, Vasim and Akash are 4/5 0.83 and 58% respectively. Who had the greatest probability of success?
Solve the following quadratic equation:$\text{x}^2-\big(\sqrt3+1\big)\text{x}+\sqrt3=0$
→In the figure, if the chord $P Q$ and chord $R S$ intersect at point $T$, prove that: $m \angle S T Q=\frac{1}{2}[m(\operatorname{arc} P R)+$ $m (\operatorname{arc} S Q)]$ for any measure of $\angle S T Q$ by filling out the boxes
Proof: $m \angle STQ = m \angle SPQ +\square \ldots$....[Theorem of the external angle of a triangle $]$ $=\frac{1}{2} m (\operatorname{arc~SQ})+\square \quad \ldots . . .[$ Inscribed angle theorem $]$
$=\frac{1}{2}[\square+\square]$
→Proof: $m \angle STQ = m \angle SPQ +\square \ldots$....[Theorem of the external angle of a triangle $]$ $=\frac{1}{2} m (\operatorname{arc~SQ})+\square \quad \ldots . . .[$ Inscribed angle theorem $]$
$=\frac{1}{2}[\square+\square]$
If x + 1, 3x and 4x + 2 are in A.P., find the value of x.
A park os of the shape of a circle of diameter 7m. it is surrounded by a path of width of 0.7m find the expenditure of cementing the path, if its cost is rs. 110 sq m.$\Big[\text{Use }\pi=\frac{22}{7}\Big]$
→Very-Short-Answer Question:
State division algorithm for polynomials.
State division algorithm for polynomials.
$\triangle \mathrm{ABC} \sim \triangle \mathrm{PQR}, \mathrm{A}(\triangle \mathrm{ABC})=16, \mathrm{~A}(\triangle \mathrm{PQP})=25$, then find the value of ratio $\frac{\mathrm{AB}}{\mathrm{PQ}}$.
→Find the nature of the roots of the following quadratic equations:$5x^2 - 4x + 1 = 0$
→Write the standard form of a linear polynomial with real coefficients.
In figure 3.78, chord MN and chord RS intersect at point D.
(1) If RD = 15, DS = 4, MD = 8 find DN
(2) If RS = 18, MD = 9, DN = 8 find DS
(1) If RD = 15, DS = 4, MD = 8 find DN
(2) If RS = 18, MD = 9, DN = 8 find DS