If sin θ - cos θ = 0, then the value of (sin⁴ θ + cos⁴ θ) is ___________

(a)

1

(b)

\(\frac{3}{4}\)

(c)

\(\frac{1}{2}\)

(d)

\(\frac{1}{4}\)

The value of sin² θ + \(\frac { 1 }{ 1+{ tan }^{ 2 }\theta } \) of ___________

(a)

sin²θ

(b)

cos²θ

(c)

secθ

(d)

1

(cosec²θ - cot²θ) (1 - cos²θ) is equal to ___________

(a)

cosec θ

(b)

cos²θ

(c)

sec²θ

(d)

sin²θ

9 sec²A  - 9tan²A = ___________

(a)

1

(b)

9

(c)

8

(d)

0

If sin (A - B) = \(\frac12\),  cos (A + B) = \(\frac12\), 0^o < A + ≤  90°, A > B, find A and B.

Express the ratios cos A, tan A and sec A in terms of sin A.

If 15tan² θ+4 sec² θ=23 then find the value of (secθ+cosecθ)² -sin² θ

The shadow of a tower, when the angle of elevation of the sum is 45^o is found to be 10 metres, longer than when it is 60^o. find the height of the tower

Express cot 85° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.

From a point on a bridge across a river, the angles of depression of the banks on opposite sides at the river are 30° and 45°, respectively. If the bridge is at a height at 3 m from the banks, find the width at the river.