Math, asked by pabitrasarkar566, 7 months ago

If sinA - cosA = 0 and sec A + cosec A = x then what is the value of x​

Answers

Answered by ItzArchimedes
3

Solution :-

Given ,

  • sinA - cosA = 0
  • secA + cosecA = x

We need to find ,

  • x = ?

◉ sinA - cosA = 0 eq(1)

◉ secA + cosecA = x eq(2)

By simplifying the given equation 1 ,

⇒ sinA - cosA = 0

⇒ sinA = cosA

Substituting ,

  • cosA = sin ( 90° - A )

⇒ sinA = sin ( 90° - A )

By comparing ,

⇒ A = 90° - A

⇒ A + A = 90°

⇒ 2A = 90°

A = 45°

Now , substituting the value of A in equation 2 ,

⇒ sec45° + cosec45° = x

⇒ √2 + √2 = x

x = 22

Hence , x = 22

Answered by tyrbylent
0

Answer:

2√2

Step-by-step explanation:

cos β = sin (90° - β)

sin A - cos A = 0

sin A = cos A

sin A = sin (90° - A) ⇒ A = 90° - A ⇒ 2A = 90° ⇒ A = 45°

sin 45° = cos 45° = (√2)/2

sec 45° = cosec 45° = 2/√2 = (2√2)/2 = √2

sec 45° + cosec 45° = 2√2

Thus, if sin A - cos A = 0, then sec A + cosec A = 2√2

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