Visualisation of Trigonometric Ratios Using a Unit Circle

Q. Sin theta + cos theta = root 2 then evaluate tan theta +cot theta

Q.

$\frac{1}{1+ta{n}^2\theta }+\frac{1}{1+co{t}^2\theta }=$

1. -1

2. 0

3. 1

4. 2

Q. Sin (1+ tan ) + cos (1+ cot)= sec + cosec.

Q.

How do you prove $\cos 2x=1-2{\sin }^{2}x$ using other trigonometric identities?

Q.

If sin A - cos A is equal to 1/2 then find the value of one upon sin a + cos A

Q.

If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that :

$x^2+y^2+z^2=r^2$

Q. In Fig. 3, from an external point P, two tangents PT and PS are drawn to a circle with centre O and radius r. If $OP=2r$, show that $\angle OTS=\angle OST={30}^{\circ }$.

Q.

If sin theta +cos theta= root 2

Evaluate. Tan theta +cot theta

Q.

If $\frac{cosa}{cosb}=mand\frac{cosa}{sinb}=n,showthat:(m^2+n^2)co{s}^{2}b=n^2.$

Q.

1 + $ta{n}^{2}A$ = $se{c}^{2}A$ is valid for which of the following ranges

1. 0 $<$ A $<$ 90

2. 0 $<$ A $\le$ 90

3. 0 $\le$ A $<$ 90

4. 0 $\le$ A $\le$ 90

Q. If $\frac{cosB}{sinA}=nand\frac{cosB}{cosA}=m,$ then show that $(m^2+n^2)co{s}^{2}A=n^2.$

Q.

If cos A= 2 sin A, then the value of cosec A is

1. -5

2. ±5

3. 

4. 5

Q.

If $x=rsinAcosB,y=rsinAsinBandz=rcosA,thenprovethat:x^2+y^2+z^2=r^2$

Q.

prove that ( 1 + cot a - cosec a ) ( 1 + tan a + sec a) = 2

Q. Explain trigonometry identities

Q.

If $sin\theta +si{n}^2\theta =1$, then find the value of $co{s}^4\theta +co{s}^2\theta -1$.

1. 2
2. 1
3. 0
4. -1

Q.

What is the value of 45 degrees if the value of 180 degrees is equal to pi?

1. pi/4

2. pi/2

3. 3pi/4

4. pi

Q. Evaluate :
${(sin\theta +cosec\theta )}^2+{(cos\theta +sec\theta )}^2$

Q.

If $7si{n}^2\theta +3co{s}^2\theta =4$, then $sec\theta +cosec\theta$ is equal to

1. $\frac{2}{\sqrt{3}}-2$

2. $\frac{2}{\sqrt{3}}+2$

3. $\frac{2}{\sqrt{3}}$

4. None of these

Q.

What is the value of PB if OP = 1 unit and $\angle POQ=\theta$?

1. $sec\theta$

2. $tan\theta$

3. $sin\theta$

4. $cot\theta$

Q.

State True or False:
In the given figure, if OP = 1 unit and ∠POQ=θ, then AP represents $tan\theta$.

1. False

2. True

Q.

SecA . √1-sin^2 A

Q. Prove that:
$\frac{\tan \theta }{(1+{\tan }^2\theta {)}^2}+\frac{\cot \theta }{(1+{\cot }^2\theta {)}^2}=\sin \theta .\cos \theta$

Q. Find the value of $x$ (in deg.) , if $\sin 2x$ = $\sin {60}^{\circ }\cos {30}^{\circ }-\cos {60}^{\circ }\sin {30}^{\circ }$

Q.

In a right angled triangle ABC (right angled at B),

the value of tan A ✕ tan C = _______.

1. 1
2. 2
3. 5
4. 10

Q.

Refer to the following figure:

∠BCA = ∠EFD. Find EF.

1. $\frac{h^2}{d}$

2. $\frac{2h}{d}$

3. $\frac{h}{d}$

4. $\frac{d^2}{h}$

Q.

State whether the given statement is true or false:

$\cot$(90-$\theta$) = $\tan$ $\theta$

1. True

2. False

Q.

A solution of the equation $cose{c}^2\theta$ + $co{t}^2\theta$ = 3 is ....................

Q. Prove that : ${\cos }^{4}A-{\cos }^{2}A={\sin }^{4}A-{\sin }^{2}A$

Q.

Refer to the following figure:

∠BCA = ∠EFD. Find EF.

1. $\frac{h^2}{d}$

2. $\frac{2h}{d}$

3. $\frac{h}{d}$

4. $\frac{d^2}{h}$