Please answer them before 10 am (indian time) and i will mark them as brainlist. Answer from section B. Fast.FAST PLEASE VERY URGENT!
Answers
Answer::
TRIGONOMETRIC REDUCTIONS ★
Given that :
Sin θ = Cos θ
Possible for only one set
θ = π / 4
Now , required value : 2Tanθ + Cos²θ
2 Tan45° + Cos²45°
2 ( 1 ) + 1/2
5/2
W
2) This is related to Trigonometric Ratios of Complementary Angles.
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As we know that two angles are said to be complementary if their
sum equals 90° .
i ) sin ( 90 - A ) = cos A
ii ) cos ( 90 - A ) = sin A
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According to the problem ,
a ) sin ( x - 20 ) = cos ( 3x - 10 )
⇒ sin ( x - 20 ) = sin [ 90 - ( 3x - 10 ) ]
⇒ x - 20 = [ 90 - ( 3x - 10 ) ]
⇒ x - 20 = 90 - 3x + 10
⇒ x + 3x = 90 + 10 + 20
⇒ 4x = 120
⇒ x = 120 / 4
∴ x = 30°
Or
sin ( x - 20 ) = cos ( 3x - 10 )
⇒ cos [ 90 - ( x - 20 ) ] = cos ( 3x - 10 )
⇒ 90 - ( x - 20 ) = 3x - 10
⇒ 90 - x + 20 = 3x - 10
⇒ 110 - x = 3x - 10
⇒ 110 + 10 = 3x + x
⇒ 120 = 4x
∴ 4x = 120
x = 120 / 4
x = 30°
I hope this helps you.
3) √3 sinθ = cosθ
sinθ = cosθ / √3
sinθ / cosθ = 1 / √3
Tanθ = 1 / √3
Tanθ = Tan30
θ = 30°
I hope that it will help you ...
