State whether the given statement is true or false-90-tan-

The correct option is A True Consider the right angled ΔABC in the figure below tan θ = AC/AB cot ∠ACB = AC/AB ∴ cot ∠ACB = tan θ But, ∠ACB + θ + 90^∘ = 180 ...

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Byju's Answer

Standard X

Mathematics

Visualisation of Trigonometric Ratios Using a Unit Circle

State whether...

Question

State whether the given statement is true or false:

$cot$ (90- $θ$ ) = $tan$ $θ$

True

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False

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Solution

The correct option is A
True

Consider the right angled $Δ A B C$ in the figure below

$t a n θ = \frac{A C}{A B} c o t ∠ A C B = \frac{A C}{A B} ∴ c o t ∠ A C B = t a n θ B u t, ∠ A C B + θ + 90^{\circ} = 180^{\circ} \Rightarrow ∠ A C B = 90^{\circ} - θ . ∴ c o t (90 - θ) = t a n θ$

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Similar questions

Q. State whether the following statement is true or false.

\frac{tan θ}{1 - cot θ} + \frac{cot θ}{1 - tan θ} = 1 + tan θ + cot θ

State whether the given statement is true or false

\sqrt{\frac{1 + sin θ}{1 - sin θ}} = sec θ - tan θ, - \frac{π}{2} < θ < \frac{π}{2}

State whether true or false

sec θ - tan θ = 8

Then

sec θ + tan θ = \frac{1}{8}

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sec θ - tan θ = 3

Then

sec θ + tan θ = - 3

State true or false. The value of expression $t a n θ - c o t θ a t θ = 30^{\circ}$ is 1.

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State whether the given statement is true or false: cot(90-θ) = tan θ

The correct option is A True Consider the right angled ΔABC in the figure below tanθ=ACABcot∠ACB=ACAB∴cot∠ACB=tanθBut, ∠ACB+θ+90∘=180∘⇒∠ACB=90∘−θ.∴cot(90−θ)=tanθ

State whether the given statement is true or false:

$cot$ (90- $θ$ ) = $tan$ $θ$