Question : If $\cos A = \sin ^2A$, and $a \sin ^{12}A+b \sin ^{10}A+c \sin ^{8}A+ \sin ^{6}A=1$, then $a + b + c$?
Option 1: 7
Option 2: 8
Option 3: 9
Option 4: 6
Correct Answer: 7
Solution : $\cos A = \sin^2A$ Square both sides, $⇒\cos^2A = \sin^4A$ $⇒1 - \sin^2A = \sin^4A$ $⇒1 = \sin^4A + \sin^2A$ Cubing both sides, $⇒1 =(\sin^4A + \sin^2A)^3$ $⇒1 = \sin^{12}A + \sin^6A + 3\sin^8A + 3\sin^{10}A$ Comparing this with the given expression, $a \sin^{12}A + b \sin^{10}A + c \sin^8A + \sin^6A = 1$, We can see that $a = 1$, $b = 3$, and $c = 3$. So, $a + b + c = 1 + 3 + 3 = 7$ Hence, the correct answer is 7.
Application | Eligibility | Selection Process | Result | Cutoff | Admit Card | Preparation Tips
Question : If $\cos A + \cos B + \cos C = 3$, then what is the value of $\sin A + \sin B + \sin C$?
Option 1: $1$
Option 2: $2$
Option 3: $0$
Option 4: $-1$
Question : If $\sin A+\sin ^2 A=1$, then the value of $\cos ^4 A+\cos ^6 A$ is:
Option 1: $\cos A$
Option 2: $\sin A$
Option 3: 1
Option 4: 0
Question : If A : B = 3 : 4 and B : C = 6 : 5, then A : ( A + C) is equal to:
Option 1: 9 : 10
Option 2: 10 : 9
Option 3: 9 : 19
Option 4: 19 : 9
Question : If $21 \tan \theta=20$, then $(1+\sin \theta+\cos \theta):(1-\sin \theta+\cos \theta)=$?
Option 1: 5 : 2
Option 2: 3 : 1
Option 3: 7 : 3
Option 4: 2 : 1
Question : If $a + b = 10$ and $ab = 9$, then the value of $a - b$ is:
Option 2: 5
Option 3: 8
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile