Question

If sin theta - cos theta = 0, and sec theta + cosec theta = x, then what is the value of x

Ans. :- 2√2

Answer 1

Solution :

Here I am using A instead of theta.

Given 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

Therefore ,

x = 2√2

••••••

Answer 2

⭐⭐⭐⭐⭐ ANSWER ⭐⭐⭐⭐⭐

Let us consume theta to be "p".

Now proceed.

Given, sin p - cos p = 0

=> (sin p - cos p)² = 0²

=> sin²p + cos²p = 2 sin p cos p

=> 1/2 = sin p cos p

Also, (sin p + cos p)²

= sin²p + cos²p + 2 sin p cos p

= 1 + 2 (1/2)

= 1 + 1

= 2

Therefore, (sin p + cos p) = √2

Now, sec p + cosec p = x

=> 1/cos p + 1/sin p = x

=> (sin p + cos p) / sin p cos p = x

=> 2√2 = x


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⭐⭐⭐ ALWAYS BE BRAINLY ⭐⭐⭐

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