Differentiation Using Substitution

Q. 58.if y= sin(4x + 2π/3) then find the value of dy/dx

Q. If tan x = x-1/4x then sec x - tan x is equal to

Q.

The period of the function y = tan x is

1. 2π

2. π

3. not defined

Q. If 12 sin x − 9sin² x attains its maximum value at x = α, then write the value of sin α.

Q.

If $\theta$is an acute angle between the lines y=2x+3, y=x+1 then the value of tan$\theta$ =

1. 2/3

2. 1/3

3. 3/4

4. 1/2

Q. If $y=si{n}^{-1}\frac{\sqrt{(1+x)}+\sqrt{(1-x)}}{2}$, then $\frac{dy}{dx}=$

1. $\frac{1}{\sqrt{(1-x^2)}}$
2. $-\frac{1}{\sqrt{(1-x^2)}}$
3. $-\frac{1}{2\sqrt{(1-x^2)}}$
4. None of these

Q. Prove that tan20^°+2tan50^°=tan70^°

Q. tan–1(tan 19) is equal to

Q. 56. tan 4theta tan 2theta = 1 then tan 3theta=? 1) 1 2)0 3)1/root3 4) root3

Q.

If $\sqrt{1-x^{2n}}+\sqrt{1-y^{2n}}=a(x^n-y^n)$ then $\sqrt{\frac{1-x^{2n}}{1-y^{2n}}}.\frac{dy}{dx}=$

1. $1$

2. $\frac{x}{y}$

3. $\frac{x^{n-1}}{y^{n-1}}$

4. $\frac{y}{x}$

Q. How to Derive the derivative of secx

Q. $Ify=\sqrt{\left(\frac{1+cos2\theta }{1-cos2\theta }\right)},\frac{dy}{d\theta }at\theta =\frac{3\pi }{4}is$

1. $-2$
2. $2$
3. $\pm 2$
4. None of these

Q. express tan4A in terms of tan A

Q. 47.y=Sin(2x) , y=sin(x^2) Differentiate

Q. 33. What is period of |sin x + cos x|

Q. Prove that:

$\sqrt{2+\sqrt{2+2\cos 4\theta }}=2\cos \theta$

Q. If tan θ + sec θ =e^x, then cos θ equals

(a) $\frac{e^x+e^{-x}}{2}$
(b) $\frac{2}{e^x+e^{-x}}$
(c) $\frac{e^x-e^{-x}}{2}$
(d) $\frac{e^x-e^{-x}}{e^x+e^{-x}}$

Q. If 3 sin x + 4 cos x = 5, then 4 sin x − 3 cos x =
(a) 0
(b) 5
(c) 1
(d) None of these

Q. If tan $\mathrm{\alpha }=\frac{1}{1+2^{-x}}$and $\tan \mathrm{\beta }=\frac{1}{1+2^{x+1}}$, then write the value of α + β lying in the interval $\left(0,\frac{\mathrm{\pi }}{2}\right)$.

Q. evaluate: lim x-->0 sin(2+x)-sin (2-x)/x

Q. Tan(π÷4+α)+Tan(3π÷4+α) = -1

Q. 44 tan + cot = 2 sin = ?

Q. 22. If y=sin (wr-kx) then the value of dy/dx is

Q. the smallest positive root of the equation †an x-x=0 lies

Q. $\int \frac{x{\sin }^{-1}x}{\sqrt{1-x^2}}dx=$
(1) $x+\sqrt{1-x^2}{\sin }^{-1}x+c$ (2) $x-{\sin }^{-1}x+c$
(3) $x-\sqrt{1-x^2}{\sin }^{-1}x+c$ (4) $\frac{x^2}{2}{\sin }^{-1}x-\sqrt{1-x^2}+c$

Q. Sin x +cos x = 1/5 then tan x/2 is equal to

Q. Express sin5A in terms of cosA.

Q. If the first derivative of the function $f\left(x\right)=\sin ({\cos }^{-1}(\frac{1-2^{2x}}{1+2^{2x}}))$ with respect to $x$ at $x=1$ is $\frac{-b}{a}\log 2,$ where $a,b$ are coprime, then $|4b-2a|=$

Q.

If $y=si{n}^{-1}(x\sqrt{1-x}+\sqrt{x}\sqrt{1-x^2})$ then $\frac{dy}{dx}=$

1. $\frac{-2x}{\sqrt{1-x^2}}+\frac{1}{2\sqrt{x-x^2}}$

2. $\frac{-1}{\sqrt{1-x^2}}-\frac{1}{2\sqrt{x-x^2}}$

3. $\frac{1}{\sqrt{1-x^2}}+\frac{1}{2\sqrt{x-x^2}}$

4. $Noneofthese$

Q. If $co{s}^{-1}\left(\frac{x^2-y^2}{x^2+y^2}\right)=loga$ then $\frac{dy}{dx}$ is equal to

1. $\frac{y}{x}$
2. $\frac{x}{y}$
3. $\frac{x^2}{y^2}$
4. $\frac{y^2}{x^2}$