Question

If sinθ = 5/13 where θ<90°, find the value of tan⁡θ + 1/cos⁡θ

answer ASAP with steps

Answer 1

Answer:

Solution: sinθ = 5/13 [Given]

∴ cosecθ = 1/sinθ = 1÷ (5/13)

∴ cosec θ = 13/5

We know that,

sin2θ + cos2θ = 1

∴ (5/13)2 + cos2θ = 1

∴ 25/169 + cos2θ = 1

∴ cos2θ= 1 – 25/169

∴ cos2θ = (169 – 25 )/169

∴ cos2θ= 144/169

∴ cosθ = ±√ (144/169)

∴ cosθ = ±12/13

But, θ is an acute angle [Given]

∴ All trigonometric ratios must be positive,

∴ cosθ = 12/13

secθ = 1/cosθ

∴ sec θ = 1÷ (12/13)

∴ secθ = 13/12

tanθ = sinθ ÷ cosθ

∴ tanθ = 5/13 ÷ 12/13

∴ tan θ = 5/13 × 13/12.

∴ tanθ = 5/12

cotθ = 1/tanθ

∴ cot θ = 1÷ (5/12)

∴ cot θ = 12/5