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:
240°
Find the radian measure corresponding to the following degree measure:
520°
Find the degree measure corresponding to the following radian measure (Use `pi = 22/7`)
-4
Find the degree measures corresponding to the following radian measures (Use `pi = 22/7`)
`(5pi)/3`
In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.
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
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:
(−3)c
Find the degree measure corresponding to the following radian measure:
11c
Find the radian measure corresponding to the following degree measure:
300°
Find the radian measure corresponding to the following degree measure: 125° 30'
The difference between the two acute angles of a right-angled triangle is \[\frac{2\pi}{5}\] radians. Express the angles in degrees.
Find the magnitude, in radians and degrees, of the interior angle of a regular pentagon.
Find the magnitude, in radians and degrees, of the interior angle of a regular octagon.
Find the magnitude, in radians and degrees, of the interior angle of a regular duodecagon.
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 angles of a triangle are in A.P. such that the greatest is 5 times the least. Find the angles in radians.
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.
Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm.
If D, G and R denote respectively the number of degrees, grades and radians in an angle, the
At 3:40, the hour and minute hands of a clock are inclined at
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
If θ lies in the second quadrant, then show that `sqrt((1 - sin theta)/(1 + sin theta)) + sqrt((1 + sin theta)/(1 - sin theta))` = −2sec θ
Find the value of tan 9° – tan 27° – tan 63° + tan 81°
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°
State whether the statement is True or False? Also give justification.
One value of θ which satisfies the equation sin4θ - 2sin2θ - 1 lies between 0 and 2π.
