MCQ
If $\sin\theta+\sin^2\theta=1$ then $\cos^2\theta+\cos^4\theta$ :
- A$-1$
- ✓$1$
- C$0$
- DNone of these.
✓
Answer
Correct option: B.
$1$
$\sin\theta+\sin^2\theta=1$
$\Rightarrow\ \sin\theta=1-\sin^2\theta$
$\Rightarrow\ \sin\theta=\cos^2\theta$
$\cos^2\theta+\cos^4\theta=\sin\theta+\sin^2\theta\ \{\because \cos^2\theta=\sin\theta\}$
$\Rightarrow\ \cos^2\theta+\cos^4\theta=1$
$\{\because \sin\theta+\sin^2\theta=1(\text{given})\}$
$\Rightarrow\ \sin\theta=1-\sin^2\theta$
$\Rightarrow\ \sin\theta=\cos^2\theta$
$\cos^2\theta+\cos^4\theta=\sin\theta+\sin^2\theta\ \{\because \cos^2\theta=\sin\theta\}$
$\Rightarrow\ \cos^2\theta+\cos^4\theta=1$
$\{\because \sin\theta+\sin^2\theta=1(\text{given})\}$
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
The perimeter of the triangle formed by the points (0, 0), (0, 1) and (0, 1) is:
Find the least number which when divided by 12 , leaves a remainder of 7 , when divided by 15 , leaves a remainder of 10 and when divided by 16 , leaves a remainder of 11 .
Choose the correct answer from the given four options:
The value of c for which the pair of equations cx - y = 2 and 6x - 2y = 3 will have infinitely many solutions is:
The value of c for which the pair of equations cx - y = 2 and 6x - 2y = 3 will have infinitely many solutions is:
The positive value of $k$ for which the equation $x^2+ kx + 64 = 0$ and $x^2- 8x + k = 0$ will both have real roots, is :
→If $\alpha, \beta$ are the zeros of the polynomial $f(x)=x^2-p(x+1)-c$ such that $(\alpha+1)(\beta+1)=0$, then $c=$
→The area of the triangle formed by the lines $x = 3, y = 4$ and $x = y$ is :
→→
A coin is tossed thrice. The probability of getting at least two tails is
Figure show the graph of the polynomial $f(x) = ax^2+ bx + c$ for which :
→The pair of equations $x=a$ and $y=b$ graphically represents lines which are:
→