Say true or false - If tan A-B-3 and -3tan A-B-1- then A-45-A- TrueB- False

The correct option is A True If tan(A + B ) = √(3) ⇒ A + B = 60^o.................(i) and √(3) tan(A B) = 1 ⇒ A B = 1/√(3) ⇒ 30^o............(ii) Addi ...

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Byju's Answer

Standard IX

Mathematics

Values of Trigonometric Ratios

Say true or f...

Question

Say true or false : If tan(A + B ) = $\sqrt{3}$ and $\sqrt{3}$ tan(A - B) = 1, then A = $45^{o}$

True

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False

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Solution

The correct option is A
True

If tan(A + B ) = $\sqrt{3}$ $\Rightarrow$ A + B = $60^{o}$ .................(i)

and $\sqrt{3}$ tan(A - B) = 1 $\Rightarrow$ A - B = $\frac{1}{\sqrt{3}} \Rightarrow 30^{o}$ ............(ii)

Adding (i) and (ii) we get

2A = 90 $\Rightarrow$ A = $45^{o}$

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Say true or false : If tan(A + B ) = √3 and √3 tan(A - B) = 1, then A = 45o

The correct option is A True If tan(A + B ) = √3 ⇒ A + B = 60o.................(i) and √3 tan(A - B) = 1 ⇒ A - B = 1√3 ⇒ 30o............(ii) Adding (i) and (ii) we get 2A = 90 ⇒ A = 45o

Say true or false : If tan(A + B ) = $\sqrt{3}$ and $\sqrt{3}$ tan(A - B) = 1, then A = $45^{o}$

The correct option is A
True

If tan(A + B ) = $\sqrt{3}$ $\Rightarrow$ A + B = $60^{o}$ .................(i)

and $\sqrt{3}$ tan(A - B) = 1 $\Rightarrow$ A - B = $\frac{1}{\sqrt{3}} \Rightarrow 30^{o}$ ............(ii)

Adding (i) and (ii) we get

2A = 90 $\Rightarrow$ A = $45^{o}$