Trigonometric Ratio(sin,cos,tan)

Q. 29. In an acute angled triangle ABC, if sin(A+B-C)=1/2 and cos(B+C-A)=1/2, find angle A, B, and C.

Q. If Sec A + tan A=x then sec A=?

Q. 1+cos theta +sin theta /1+cos theta - sin theta =1+sin theta /cos theta. Prove the above .

Q. cosec⁶A - cot ⁶A = 3 cot²A * cosec²A +1

Emergency. PROVE LHS = RHS

Q. If theta =1/3, then find the value of cos theta

Q. A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height 5 meters. At a point on the plane, the angles of elevation of the bottom and the top of the flag staff are respectively 30° and 60°. Find the height of the tower.

1. 
   2.5 m
2. 
   5 m
3. 
   3.2 m
4. 
   3 m

Q. 10. Prove that tan square A +cot square A =sec square A cosec square A-2

Q. If $sin\theta =\frac{20}{29}$, find $cos\theta$.

1. $\frac{9}{29}$
2. $1$
3. $\frac{20}{29}$
4. $\frac{21}{29}$

Q. 7. If 7 cosec A - 3 cot A = 7 , prove that 7 cot A - 3 cosec A = 3.

Q. 9. If sin theta + cos theta =root 2 sin theta, then show that sin theta-cos theta = root 2 sin theta.

Q. Prove that cos6x= 32cos⁶x-48cos⁴x+18 cos²x-1

Q. Express sin theta in terms of cot theta

Q. Differentiation of log(tan(x/2))

Q. In the ∆PQR, right angled at Q, QR=9 cm and PR-PQ =1 cm. Determine the value of sin R + cos R.

Q.

What is the ratio for sine of theta?

Q.

From the figure, the value of cosec A + cot A is :

1. 

2. 

3. 

4. 

Q.

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

The value of tan A tan C=__

Q.

In a right triangle ABC right-angled at C, P and Q are the points on the sides CA and CB respectively, which divide these sides in the ratio 2:1.


Prove that [4 MARKS]

(i) $9A{Q}^2=9{AC}^2+4{BC}^2$

(ii) $9{BP}^2=9{BC}^2+4{AC}^2$

(iii) $9({AQ}^2+{BP}^2)=13{AB}^2$

Q. In a $△$ABC, right angled at B, AB + AC = 25 units, and BC = 5 units.
What is $\sin C$?

Q. sinA +sin2A/1+cosA+cos2A is equal to

Q. 6. prove that: 1+sin2A/cos2A=cosA+sinA/cosA-sinA

Q. if y= a(1-cos theta) and x=a(theta+sin theta) then find the value of dy/dx at theta =pie/2

Q.

If 3 cos θ = 1, then the value of cosec θ is :

1. 

2. 

3. 

4. 

Q. cosec a + cot a =3 find cos a

Q.

If x = 2sin² θ, y = 2cos² θ + 1, then the value of x + y is:

1. 3

2. 2

3. 1

4. 

Q. Tan theta+ sec theta =7 then Tan theta - sec theta=?

Q. If A+B+C=45 ° , then the value of ∑(†an A+†an A†an B) is

Q.

What is the trigonometric ratio that connects the opposite side to adjacent side in a right-angled triangle?

1. $cos\theta$

2. $tan\theta$

3. $sin\theta$

4. $sec\theta$

Q. how to simplify (sinAcosB+cosAsinB)/(cosAcosB-sinAsinB) to (tanA+tanB)/(1-tanAtanB)?

Q.

Prove that

Cot^{​​​​2} ​​​​​​A × cosec^​​2​A - cot^{​​​​2}​​​B × cosec^​​2 B = cot^{​​​​2}​​​A - cot^{​​​​2} B