If cosec θ + cot θ = x, find the value of cosec θ – cot θ

Write the values of sec 0°, sec 30°, sec 45°, sec 60° and sec 90°. What happens to sec x when x increases from 0° to 90° ?

Question 7.
If sin θ = 12/13, 0° < θ < 90°, find the value of: sin² θ- cos² θ /2 sin θ. cos θ  x 1/tan² θ

Question 8.
If sin (A + B) = 1 and tan (A – B) = 1/√3, find the value of:

1. tan A + cot B
2. sec A – cosec B

If sec A = x +\( \frac{1}{4x} \), prove that sec A + tan A = 2x or \( \frac{1}{2x} \)

Question 12.
If sec θ – tan θ = x, show that: sec θ=1/2(x+1/x) and tan θ=1/2(1/x-x)

Evaluate: sin θ.sec(90 – θ)

Question 15.
Prove the following identity:sin³ θ+cos³ θ/sin θ+cos θ= 1 – sin θ.cos θ

If 7sin²A + 3cos²A = 4, show that tan A =\( \frac{1}{√3} \)

For any acute angle θ, prove that

1. sin²θ + cos²θ = 1
2. 1 + cot²θ = cosec²θ

If cosec θ = 5/3, then what is the value of cos θ + tanθ

Find the value of tan(65° – θ) – cot(25° + θ)

Find the value of cos θ + sec θ, when it is given that cos θ =1/2

Evaluate: 3 cot² 60° + sec² 45°.

Solve the equation for θ: 

If A, B, and C are the interior angles of a ΔABC, show that 

If tan θ + cot θ= 2, find the value of 

If cosec A + cot A = m, show that 

Question 37.
Prove that: (sec θ + tan θ)² = cosec θ +1/cosec θ -1

If cosec θ + cot θ = q, show that cosec θ – cot θ = \( \frac{1}{q} \) and hence find the values of sin θ and sec θ

ΔRPQ is a right-angled at Q. If PQ = 5 cm and RQ = 10 cm, find:

1. sin²P
2. cos²R and tan R
3. sin P x cos P
4. sin²P – cos²P
   

If sin A = cos A, find the value of 2tan² A + sin² A – 1

If sec θ + tan θ = p, then find the value of cosecθ

Evaluate: 4/Cot² 30°+1/sin² 60°-cos² 45°

Evaluate: 4(sin⁴30° + cos⁴60°) – 3(cos²45°-sin²90°)

In an acute angled triangle ABC, if sin (A + B – C) =\( \frac{1}{2} \) and cos (B + C – A) = 1/\( \frac{1}{√2} \) find ∠A, ∠B and ∠C

Prove that: =2 secA

If cos θ-sin θ=√2 sin θ, prove that cos θ+sin θ=√2 cos θ

Find the value of sec 60° geometrically

Find the value of sec 45° geometrically

Prove that: (cosec θ – sin θ). (sec θ – cos θ) =cot θ

Prove that: (1 + cot A – cosec A) (1 + tan A + sec A) = 2.

Prove that: sin θ (1 + tan θ) + cos θ (1 + cot θ) = sec θ + cosec θ.

If sec A = \( \frac{15}{7} \) and A + B = 90°, find the value of cosec B