In ΔABC, m∠B = 90. If BC = 3 and AC = 5, find all the six trigonometric ratios of ∠A.

If sinB = prove that 3cosB – 4cos³B = 0.

State whether the following are true or false. Justify your answer:

(1) sin θ = , for some angle having measure θ.

(2) cos θ = , for some angle having measure θ.

(3) cosecA = for some measure of angle A.

(4) The value of tanA is always less than 1.

(5) secB = for some ∠B.

(6) cos θ = 100 for some angle having measure θ.

If tan θ = , find the value of

In ΔABC, m∠C = 90 and m∠A = m∠B,

(1) Is cosA = cosB?

(2) Is tanA = tanB?

(3) Will the other trigonometric ratios of ∠A and ∠B be equal?

If cos θ = , verify that tan²θ – sin²θ = tan²θ⋅ sin²θ

If pcot θ = q, examine whether

If 3cotA = 4, examine whether cos²A – sin²A.

If tanA = √3, verify that

(1) sin²A + cos²A = 1

(2) sec²A – tan²A = 1

(3) 1 + cot²A = cosec²A

If sec θ = find the value of

In ΔABC, m∠A = 90 and if AB : BC = 1 : 2 find sinB, cosC, tanC.