If tan70-tan20-2tan A-then the value of A is in degree

Tan70^∘=tan(20^∘+50^∘) ⇒ nbsp;tan70^∘=tan20^∘+tan50^∘1 tan20^∘tan50^∘ ⇒ nbsp;tan70^∘ tan70^∘tan20^∘tan50^∘=tan20^∘+tan50^∘ ⇒ nbsp;tan70^∘ tan(90^∘ 20^∘)ta ...

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Standard XII

Mathematics

Trigonometric Ratios for Sum of Two Angles

If tan70∘=tan...

Question

If $tan 70^{\circ} = tan 20^{\circ} + 2 tan A^{\circ}$ ,then the value of $A$ is (in degree)

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Solution

$tan 70^{\circ} = tan (20^{\circ} + 50^{\circ}) \Rightarrow tan 70^{\circ} = \frac{tan 20^{\circ} + tan 50^{\circ}}{1 - tan 20^{\circ} tan 50^{\circ}} \Rightarrow tan 70^{\circ} - tan 70^{\circ} tan 20^{\circ} tan 50^{\circ} = tan 20^{\circ} + tan 50^{\circ} \Rightarrow tan 70^{\circ} - tan (90^{\circ} - 20^{\circ}) tan 20^{\circ} tan 50^{\circ} = tan 20^{\circ} + tan 50^{\circ} \Rightarrow tan 70^{\circ} - cot 20^{\circ} tan 20^{\circ} tan 50^{\circ} = tan 20^{\circ} + tan 50^{\circ} \Rightarrow tan 70^{\circ} - tan 50^{\circ} = tan 20^{\circ} + tan 50^{\circ} \Rightarrow tan 70^{\circ} = tan 20^{\circ} + 2 tan 50^{\circ} ∴ A = 50^{\circ}$

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If tan70∘=tan20∘+2tanA∘,then the value of A is (in degree)

If $tan 70^{\circ} = tan 20^{\circ} + 2 tan A^{\circ}$ ,then the value of $A$ is (in degree)