Question

If sin θ − cos θ = 0 (0°≤θ≤90°) and sec θ + cosec θ=x, then find x.

Answer 1

Answer:

Trigonometric equations

Step-by-step explanation:

sin Ф + cos Ф = \sqrt{2}

2

cos Ф

\frac{1}{\sqrt{2} }

2

1

sin Ф + \frac{1}{\sqrt{2} }

2

1

cos Ф = cos Ф

sin\frac{\pi }{4}

4

π

sin Ф + cos \frac{\pi }{4}

4

π

cos Ф = cos Ф

cos ( \frac{\pi }{4}

4

π

- Ф) = cos Ф

( \frac{\pi }{4}

4

π

- Ф) = Ф

Answer 2

Step-by-step explanation:

sinA - cosA = 0

=> sinA = cosA

=> sinA = sin( 90 - A )

=> A = 90 - A

=> A + A = 90

=> 2A = 90°

=> A = 45°

Now ,

x = sec A + cosec A

= sec 45° + cosec 45°

= √2 + √2

= 2√2

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