What is the value of
( cot 7 0 ∘ + 4 cos 7 0 ∘ ) 2 ?
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Absolutely Correct and really Brilliant Solution Sir
How id you change -2Sin140 to 2Cos130?
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-sin140=-sin40=-cos 50=cos130
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Can u please explain again? I didnt understand it. Thanks
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@Yousuf Khan – Okay.
First, we know that: sin 1 4 0 ∘ = sin ( 1 8 0 ∘ − 1 4 0 ∘ ) = sin 4 0 ∘ .
Then: sin 4 0 ∘ = cos ( 9 0 ∘ − 4 0 ∘ ) = cos 5 0 ∘
Finally: − cos 5 0 ∘ = cos ( 1 8 0 ∘ − 5 0 ∘ ) = cos 1 3 0 ∘
You can use a calculator to confirm that they are equal. I have done that with a spreadsheet.
Sin(270-130)= -Cos130
That's call brilliant..
That's absolutely Brilliant!
that is mind blowing
please show me which is formula you have used?
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Two formulas: Double Angle Formula 1. sin2θ = 2sinθcosθ Angle Addition Formula 2. cos(θ±φ)=cosθcosφ∓sinθsinφ
Prepare for a trig identity overload. Most of this will deal with what is inside the parentheses, and will be squared at the very end. All of this is performed in degrees.
Trig Identity 1: cot θ = sin θ cos θ
cot 7 0 + 4 cos 7 0 = sin 7 0 cos 7 0 + 4 cos 7 0 = sin 7 0 cos 7 0 + 4 sin 7 0 cos 7 0
Trig Identity 2: sin 2 θ = 2 sin θ cos θ
Trig Identity 3: cos ( 9 0 − θ ) = sin θ
= sin 7 0 cos ( 9 0 − 2 0 ) + 2 ( 2 sin 7 0 cos 7 0 ) = sin 7 0 sin 2 0 + 2 sin 1 4 0 = sin 7 0 sin 2 0 + sin 1 4 0 + sin 1 4 0
Trig Identity 4: sin θ + sin ϕ = 2 sin ( 2 θ + ϕ ) cos ( 2 θ − ϕ )
Unit Circle: cos 6 0 = 2 1
Unit Circle: cos 3 0 = 2 3
= sin 7 0 2 sin 8 0 cos 6 0 + sin 1 4 0 = sin 7 0 sin 8 0 + sin 1 4 0
= sin 7 0 2 sin 1 1 0 cos 3 0 = sin 7 0 3 sin 1 1 0
Trig Identity 5: sin ( 1 8 0 − θ ) = sin θ
= sin 7 0 3 sin ( 1 8 0 − 7 0 ) = sin 7 0 3 sin 7 0 = 3
This was all squared, therefore ( 3 ) 2 = 3 □
Brilliant One Sir
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cot 7 0 ∘ + 4 cos 7 0 ∘ sin 7 0 ∘ cos 7 0 ∘ + 4 cos 7 0 ∘ cos 7 0 ∘ + 4 sin 7 0 ∘ cos 7 0 ∘ cos 7 0 ∘ + 2 sin 1 4 0 ∘ cos 7 0 ∘ − k sin 7 0 ∘ cos 7 0 ∘ − k sin 7 0 ∘ cos 7 0 ∘ − k sin 7 0 ∘ cos 7 0 ∘ − k sin 7 0 ∘ cos 7 0 ∘ − k sin 7 0 ∘ ⟹ k = k = k = k sin 7 0 ∘ = k sin 7 0 ∘ = − 2 sin 1 4 0 ∘ = 2 cos 1 3 0 ∘ = 2 ( cos 6 0 ∘ cos 7 0 ∘ − sin 6 0 ∘ sin 7 0 ∘ ) = 2 ( 2 1 cos 7 0 ∘ − 2 3 sin 7 0 ∘ ) = cos 7 0 ∘ − 3 sin 7 0 ∘ = 3