Question

If sec theta = cosec theta and 0º = theta < 90°, find the value of theta.​

Answer 1

Answer:

∅= 45°. [ I am using this symbol (∅) for theta]

Step-by-step explanation:

sec ∅ = cosec ∅

1/cos ∅ = 1/sin ∅. [ since sec and cosec are reciprocals of sin and cosine]

sin ∅/cos ∅ = 1

tan ∅ = 1 [sin/cos = tan]

tan 45°=1. [the value of tan 45°=1]

So,∅=45°

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Answer 2

Answer:

45°

Step-by-step explanation:

For, 0°≤theta≤90°

sec(theta)=cosec(theta)

1/cos(theta)=1/sin(theta)

sin(theta)=cos(theta)

-take a both sides square..

-we get,

sin²(theta)=cos²(theta)

sin²(theta)=1-sin²(theta)

2sin²(theta)=1

sin²(thera)=1/2

sin(theta)=1/√2

(theta)=sin^-1 (1/√2)

(theta)=sin^-1 (sin45°)

(theta)=45°