NDA MATHEMATICS QUIZ - 24

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Question 1:

The expression $\cos ^{2}(x-y)+\cos ^{2} y-2 \cos (x-y) \cos x \cdot \cos y$ is independent of

Question 2:

If $\sin \alpha(1+\sin \alpha)+\cos \alpha(1+\cos \alpha)=\mathrm{a}$ and $\sin \alpha(1-\sin \alpha)+\cos \alpha(1-\cos \alpha)=\mathrm{b}$ then

Question 3:

If $\tan x=\frac{a}{a-1}$ and $\tan y=\frac{1}{2 a-1}$ then one of the values of $(x-y)$ is

Question 4:

If $\frac{ \sin \theta}{1+\cos \theta+\sin \theta}=x$ then value of $\frac{1-\cos \theta+\sin \theta}{1+\sin \theta}$ is equal to:

Question 5:

The equation $\cos 2 \theta+p \sin \theta=2 p-7$ has a solution

Question 6:

If $x \neq n \pi$ then value of the expression $2-4 \sin ^{2} x+3 \sin ^{4} x-\sin ^{6} x$ is equal to 1

Question 7:

If $0<\alpha<\frac{\pi}{2}$ then $\tan \alpha+\tan 2 \alpha+\tan 3 \alpha=0$ if 

Question 8:

If $\sin ^{2} \alpha=1-\sin \alpha$ then the value of $\left(\cos ^{6} \alpha+\cos ^{12} \alpha+3 \cos ^{10} \alpha+3 \cos ^{8} \alpha-1\right)$ is equal to:

Question 9:

Value of the expression $1-\frac{\sin ^{2} x}{1+\cot x}-\frac{\cos ^{2} x}{1+\tan x}$ is equal to

Question 10:

If $A_{n}=\sin ^{n} \theta+\cos ^{n} \theta$ then $\frac{A_{3}-A_{5}}{A_{1}}$ equals

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