Question

Pls help someone
All the answers

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

1) ( 1 + 1 ) / 8 ( 1/2)²- ( 1 )²

= 2 / ( 2 - 1 )

= 2

2) cos 70°/sin 20° + cos 59°/sin 31° - 8 sin²30°

= cos (90°- 20°) / sin 20° + cos ( 90°- 31°) / sin31° - 8 ( 1/2)²

= sin 20°/sin20° + sin 31°/ sin 31° - 2

= 1 + 1 - 2

= 2 - 2

= 0

4) tan ( b + c ) / 2

= tan ( 90° - a ) / 2

= cot a/2 is proved.

5) sin² x + cos² 30° = 5/4

⇒sin² x + ( √3/2)² = 5/4

⇒ sin² x + 3/4 = 5/4

⇒ sin² x = 5/4 - 3/4

⇒ sin² x = 2/4

⇒ sin² x = 1/2

⇒x = √1/2

⇒ x = ± 1/√2

⇒ x = 45°

6) 3 sin 60° + 2 cos ( 45°) / 2 cos 60° - sin ( 30°)

= 3 ( √3/2 ) + 2 ( 1/√2 ) / 2 ( 1/2 ) - 1/2

= (3√3/2 + 2√2/2 ) / ( 1 - 1/2 )

= (5√2/2) / (1/2)

= 5√2

7) tan 2x = cot ( x + 6)

⇒ cot ( 90°- x ) = cot ( x + 6 )

( 90°- x ) and ( x + 6° ) both are acute angles,

So, 90°- x = x + 6°

⇒ 2x = 90°- 6°

⇒ 2x = 84°

⇒ x = 84° / 2

⇒ x = 42°