Question : If for any acute angle A, $\sin A+\sin^{2} A=1$, then the value of $\cos^{2}A+\cos^{4}A$ is:
Option 1: –1
Option 2: 1
Option 3: 2
Option 4: 0
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 1
Solution : Given: $\sin A+\sin^{2} A=1$ ----(1) ⇒ $\sin A=1–\sin^{2} A$ ⇒ $\sin A=\cos^{2} A$ -----(2) ⇒ $\sin^{2} A=\cos^{4} A$ -----(3) From equation (2) and (3), we get: So, $\cos^{2} A+\cos^{4} A=\sin A+\sin^{2} A$ ⇒ $\cos^{2} A+\cos^{4} A=1$ Hence, the correct answer is 1.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : For any acute angle $\theta, \sin \theta+\sin^2 \theta=1$, then the value of $\cos^2 \theta+\cos^4 \theta=$___________.
Question : If $\sin \theta=\frac{1}{2}$, then the value of $\left(3 \cos \theta-4 \cos ^3 \theta\right)$ is:
Question : If $\sin \theta +\sin ^{2}\theta =1$, then the value of $\cos ^{2}\theta +\cos ^{4}\theta$ is:
Question : If $\cos A+\cos^2 A=1$, then the value of $\sin^4 A+\sin^6 A$ is:
Question : If $x=a(\sin\theta+\cos\theta), y=b(\sin\theta-\cos\theta)$, then the value of $\frac{x^2}{a^2}+\frac{y^2}{b^2}$ is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile