Question

cos^ 67 - sin^ 23 find the value

Answer 1

Hey there!

We know that,
cos²B - sin²A = cos(A + B) * cos ( A - B)

Now,
cos²67° - sin²23°
= cos(67 + 23 ) * cos( 67 - 23 )
= cos ( 90 ) * cos45
= 0 * 1/√2 .
= 0

$\therefore$ cos²67 -sin²23 = 0 .

Quick Alternative : [ cos²67-sin²23 = cos²(90-23) - sin²23 = sin²23 - sin²23 = 0 ]

[ cos²67-sin²23 = cos²67-sin²(90-67) = cos²67-cos²67 = 0 ]

Hope helped!

Answer 2

Hi.

Here is your answer---

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Given Identity---

Cos²67 - Sin²23

Using the Formula,

Cos²X - Sin²Y  =  Cos(X + Y) × Cos(X - Y)
                         =  Cos(67 + 23) × Cos(67 - 23)
                         = Cos 90° × Cos 44° [ Almost 45°]
                         = Cos 90° × Cos 45°
                         = 0 × 1/√2
                         = 0           

Thus, Cos²67° - Sin²23° = 0

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Hope it helps.


Have a nice day.