Without using trigonometrical tables- find the value of tan 1- - tan 2-tan 3-tan 89- -3 MARKS-

Formula: 1 Mark Solution: 2 Marks tan 1^∘. tan 2^∘ tan 3^∘… tan 87^∘ tan 88^∘ tan 89^∘ =tan 1^∘ tan 2^∘ tan 3^∘… cot (90^∘ 87^∘) cot(90^∘ 88^∘) cot (90^∘ ...

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Standard X

Mathematics

Trigonometric Ratios of Complementary Angles

Without using...

Question

Without using trigonometrical tables, find the value of $t a n 1^{\circ} . t a n 2^{\circ} t a n 3^{\circ} \dots t a n 89^{\circ}$ [3 MARKS]

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Solution

Formula: 1 Mark
Solution: 2 Marks

$t a n 1^{\circ} . t a n 2^{\circ} t a n 3^{\circ} \dots t a n 87^{\circ} t a n 88^{\circ} t a n 89^{\circ} = t a n 1^{\circ} t a n 2^{\circ} t a n 3^{\circ} \dots c o t (90^{\circ} - 87^{\circ}) c o t (90^{\circ} - 88^{\circ}) c o t (90^{\circ} - 89^{\circ}) = t a n 1^{\circ} t a n 2^{\circ} t a n 3^{\circ} \dots c o t 3^{\circ} c o t 2^{\circ} c o t 1^{\circ} = t a n 1^{\circ} t a n 2^{\circ} t a n 3^{\circ} \dots \frac{1}{t a n 3^{\circ}} . \frac{1}{t a n 2^{\circ}} . \frac{1}{t a n 1^{\circ}} = 1$

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Similar questions

Q. Without using trigonometric tables, evaluate the follow

{tan 1}^{0} {tan 2}^{0} {tan 3}^{0} . . . . . . . . {t a n 89}^{0}

Q. Find the value

t a n 1^{\circ} . t a n 2^{\circ} . t a n 3^{\circ} . . . . . . . . . . t a n 89^{\circ}

Q. Find the value of

t a n 1^{\circ} t a n 2^{\circ} t a n 3^{\circ}, . . . . . . . . . . . . . . . . t a n 89^{\circ}

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The value of $tan 1^{\circ} tan 2^{\circ} tan 3^{\circ} . . . . . . tan 89^{\circ}$ is

Q. The value of

tan 1^{\circ} tan 2^{\circ} tan 3^{\circ} \dots tan 89^{\circ}

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Without using trigonometrical tables, find the value of tan 1∘.tan 2∘ tan 3∘… tan 89∘ [3 MARKS]

Formula: 1 Mark Solution: 2 Marks tan 1∘.tan 2∘ tan 3∘… tan 87∘ tan 88∘ tan 89∘=tan 1∘ tan 2∘ tan 3∘…cot(90∘−87∘) cot(90∘−88∘) cot (90∘−89∘)=tan 1∘ tan 2∘ tan 3∘…cot 3∘ cot 2∘ cot 1∘=tan 1∘ tan 2∘ tan 3∘…1tan 3∘.1tan 2∘.1tan 1∘=1

Without using trigonometrical tables, find the value of $t a n 1^{\circ} . t a n 2^{\circ} t a n 3^{\circ} \dots t a n 89^{\circ}$ [3 MARKS]