Advertisements
Advertisements
Question
The value of tan1° tan2° tan3° ... tan89° is ______.
Options
0
1
`1/2`
Not defined
Advertisements
Solution
The value of tan1° tan2° tan3° ... tan89° is 1.
Explanation:
tan1° tan2° tan3°… tan89°
= tan1° tan2° … tan45° tan(90° - 44°) tan(90° - 43°) ..…tan(90° - 1°)
= tan1° tan2° … tan45° cot44° cot43° … cot1° ......[∵ tan(90° - θ) = cotθ]
= tan1° cot1° tan2° cot2°…tan45°… tan89° cot89°
= 1.1….1
= 1
APPEARS IN
RELATED QUESTIONS
Find the radian measure corresponding to the following degree measure:
– 47° 30'
Find the radian measure corresponding to the following degree measure:
240°
Find the radian measure corresponding to the following degree measure:
520°
Find the degree measures corresponding to the following radian measures (Use `pi = 22/7`)
`(5pi)/3`
If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.
Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length
10 cm
Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length
15 cm
Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length
21 cm
Find the degree measure corresponding to the following radian measure:
\[\frac{9\pi}{5}\]
Find the degree measure corresponding to the following radian measure:
\[- \frac{5\pi}{6}\]
Find the degree measure corresponding to the following radian measure:
(−3)c
Find the radian measure corresponding to the following degree measure:
300°
Find the radian measure corresponding to the following degree measure: −56°
Find the radian measure corresponding to the following degree measure: −300°
Find the radian measure corresponding to the following degree measure: 7° 30'
One angle of a triangle \[\frac{2}{3}\] x grades and another is \[\frac{3}{2}\] x degrees while the third is \[\frac{\pi x}{75}\] radians. Express all the angles in degrees.
Let the angles of the quadrilateral be \[\left( a - 3d \right)^\circ, \left( a - d \right)^\circ, \left( a + d \right)^\circ \text{ and }\left( a + 3d \right)^\circ\]
We know: \[a - 3d + a - d + a + d + a - 2d = 360\]
\[ \Rightarrow 4a = 360\]
\[ \Rightarrow a = 90\]
We have:
Greatest angle = 120°
Now,
\[a + 3d = 120\]
\[ \Rightarrow 90 + 3d = 120\]
\[ \Rightarrow 3d = 30\]
\[ \Rightarrow d = 10\]
Hence,
\[\left( a - 3d \right)^\circ, \left( a - d \right)^\circ, \left( a + d \right)^\circ\text{ and }\left( a + 3d \right)^\circ\] are
Angles of the quadrilateral in radians =
The angle in one regular polygon is to that in another as 3 : 2 and the number of sides in first is twice that in the second. Determine the number of sides of two polygons.
The number of sides of two regular polygons are as 5 : 4 and the difference between their angles is 9°. Find the number of sides of the polygons.
Find the length which at a distance of 5280 m will subtend an angle of 1' at the eye.
The radius of a circle is 30 cm. Find the length of an arc of this circle, if the length of the chord of the arc is 30 cm.
If D, G and R denote respectively the number of degrees, grades and radians in an angle, the
If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, than the ratio of the radii of the circles is
If OP makes 4 revolutions in one second, the angular velocity in radians per second is
A circular wire of radius 7 cm is cut and bent again into an arc of a circle of radius 12 cm. The angle subtended by the arc at the centre is
Find the value of tan 9° – tan 27° – tan 63° + tan 81°
Prove that `(sec8 theta - 1)/(sec4 theta - 1) = (tan8 theta)/(tan2 theta)`
If tan θ = `(-4)/3`, then sin θ is ______.
The value of cos1° cos2° cos3° ... cos179° is ______.
State whether the statement is True or False? Also give justification.
The equality sinA + sin2A + sin3A = 3 holds for some real value of A.
State whether the statement is True or False? Also give justification.
Sin10° is greater than cos10°
