Question

If 0 < A < $\frac{\pi}{4}$ and cos A = $\frac{4}{5}$, find the value of sin 2A and cos 2A.

Answer 1

cosA = 4/5 = b/h

so, b = 4 and h = 5

then, p = √(h² - b²) = √(5² - 4²) = 3

so, sinA = p/h = 3/5

now, sin2A = 2sinA cosA [ from formula ]

= 2 × 3/5 × 4/5

= (2 × 3 × 4)/(5 × 5)

= 24/25

hence, sin2A = 24/25


again, cos2A = cos²A - sin²A [ from formula]

= (4/5)² - (3/5)²

= 16/25 - 9/25

= 7/25

Answer 2

HELLO DEAR,



cosA = 4/5 = b/h

so, b = 4 and h = 5

then, p = √(h² - b²) = √(5² - 4²) = 3

so, sinA = p/h = 3/5

now, we know:-
sin2A = 2sinA cosA

=> 2 × 3/5 × 4/5

=> (2 × 3 × 4)/(5 × 5)

=> 24/25

hence, sin2A = 24/25


[as, cos2A = cos²A - sin²A ]

=> (4/5)² - (3/5)²

=> 16/25 - 9/25

=> 7/25



I HOPE IT'S HELP YOU DEAR,
THANKS