The value of ( sin 7 0 ∘ ) ( cot 1 0 ∘ cot 7 0 ∘ − 1 ) is

( sin 7 0 ∘ ) ( cot 1 0 ∘ cot 7 0 ∘ − 1 ) = sin 7 0 ∘ cot 1 0 ∘ cot 7 0 ∘ − sin 7 0 ∘ = cot 1 0 ∘ cos 7 0 ∘ − sin 7 0 ∘ = sin 1 0 ∘ cos 1 0 ∘ cos 7 0 ∘ − sin 7 0 ∘ sin 1 0 ∘ = sin 1 0 ∘ cos ( 1 0 ∘ + 7 0 ∘ ) = sin 1 0 ∘ cos 8 0 ∘ = 1

Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

MathematicsTrigonometric Ratios & IdentitiesAddition, Multiplication, Subtraction formula based,Multiple/Submultiple anglesEasy2 minPYQ_2025

MathematicsEasysingle choice

The value of $(sin 7 0^{\circ}) (cot 1 0^{\circ} cot 7 0^{\circ} - 1)$ is

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Solution:

$(sin 7 0^{\circ}) (cot 1 0^{\circ} cot 7 0^{\circ} - 1) = sin 7 0^{\circ} cot 1 0^{\circ} cot 7 0^{\circ} - sin 7 0^{\circ} = cot 1 0^{\circ} cos 7 0^{\circ} - sin 7 0^{\circ} = \frac{cos 1 0 ^{\circ} cos 7 0 ^{\circ} - sin 7 0 ^{\circ} sin 1 0 ^{\circ}}{sin 1 0 ^{\circ}} = \frac{cos ( 1 0 ^{\circ} + 7 0 ^{\circ} )}{sin 1 0 ^{\circ}} = \frac{cos 8 0 ^{\circ}}{sin 1 0 ^{\circ}} = 1$

Stream:JEESubject:MathematicsTopic:Trigonometric Ratios & IdentitiesSubtopic:Addition, Multiplication, Subtraction formula based,Multiple/Submultiple angles

⏱ 2mℹ️ Source: PYQ_2025

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