Advertisements
Advertisements
प्रश्न
The value of (tan1° tan2° tan3° ... tan89°) is ______.
पर्याय
0
1
2
`1/2`
उत्तर
The value of (tan1° tan2° tan3° ... tan89°) is 1.
Explanation:
tan 1°.tan 2°.tan 3° ...... tan 89°
= tan 1°.tan 2°.tan 3°...tan 43°.tan 44°.tan 45°.tan 46°.tan 47°...tan 87°.tan 88°.tan 89°
Since, tan 45° = 1,
= tan 1°.tan 2°.tan 3°...tan 43°.tan 44°.1.tan 46°.tan 47°...tan 87°.tan 88°.tan 89°
= tan 1°.tan 2°.tan 3°…tan 43°.tan 44°.1.tan(90° – 44°).tan(90° – 43°) ...tan(90° – 3°).tan(90° – 2°).tan(90° – 1°)
Since, tan(90° – θ) = cot θ,
= tan 1°.tan 2°.tan 3°...tan 43°.tan 44°.1.cot 44°.cot 43°...cot 3°.cot 2°.cot 1°
Since, tan θ = `(1/cot θ)`
= `tan1^circ * tan2^circ * tan3°...tan43^circ * tan44^circ * 1 * (1/tan 44^circ)`. `(1/tan 43^circ) ... (1/tan 3^circ) * (1/tan 2^circ) * (1/tan 1^circ)`
= `(tan 1^circ xx 1/tan1^circ) * (tan 2^circ xx 1/tan 2^circ) ... (tan 44^circ xx 1/tan 44^circ)`
= 1
Hence, tan 1°.tan 2°.tan 3° ...... tan 89° = 1
APPEARS IN
संबंधित प्रश्न
If sin θ =3/5, where θ is an acute angle, find the value of cos θ.
Without using trigonometric tables evaluate the following:
`(i) sin^2 25º + sin^2 65º `
`(\text{i})\text{ }\frac{\cot 54^\text{o}}{\tan36^\text{o}}+\frac{\tan 20^\text{o}}{\cot 70^\text{o}}-2`
Express each of the following in terms of trigonometric ratios of angles between 0º and 45º;
(i) cosec 69º + cot 69º
(ii) sin 81º + tan 81º
(iii) sin 72º + cot 72º
If tan A = cot B, prove that A + B = 90
Evaluate:
3cos80° cosec10° + 2 sin59° sec31°
Evaluate:
14 sin 30° + 6 cos 60° – 5 tan 45°
Find the value of x, if tan x = `(tan60^circ - tan30^circ)/(1 + tan60^circ tan30^circ)`
Prove that:
`(cos(90^circ - theta)costheta)/cottheta = 1 - cos^2theta`
Evaluate:
`(sin35^circ cos55^circ + cos35^circ sin55^circ)/(cosec^2 10^circ - tan^2 80^circ)`
Use tables to find sine of 62° 57'
Use tables to find the acute angle θ, if the value of tan θ is 0.7391
Find A, if 0° ≤ A ≤ 90° and 2 cos2 A – 1 = 0
If 3 cos θ = 5 sin θ, then the value of
The value of \[\frac{\cos^3 20°- \cos^3 70°}{\sin^3 70° - \sin^3 20°}\]
If ∆ABC is right angled at C, then the value of cos (A + B) is ______.
In the case, given below, find the value of angle A, where 0° ≤ A ≤ 90°.
cos(90° - A) · sec 77° = 1
Find the value of the following:
`(cos 70^circ)/(sin 20^circ) + (cos 59^circ)/(sin31^circ) + cos theta/(sin(90^circ - theta))- 8cos^2 60^circ`
Prove that `"tan A"/"cot A" = (sec^2"A")/("cosec"^2"A")`
