Advertisements
Advertisements
प्रश्न
The value of tan1° tan2° tan3° ... tan89° is ______.
पर्याय
0
1
`1/2`
Not defined
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the radian measure corresponding to the following degree measure:
25°
Find the radian measure corresponding to the following degree measure:
– 47° 30'
Find the degree measure corresponding to the following radian measure (use `pi= 22/7`).
`(7pi)/6`
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 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:
11c
Find the degree measure corresponding to the following radian measure:
1c
Find the radian measure corresponding to the following degree measure:
300°
Find the radian measure corresponding to the following degree measure: 35°
Find the radian measure corresponding to the following degree measure: 7° 30'
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.
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.
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 heptagon.
Find the magnitude, in radians and degrees, of the interior angle of a regular duodecagon.
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 angles of a triangle are in A.P. such that the greatest is 5 times the least. Find the angles in radians.
Find the length which at a distance of 5280 m will subtend an angle of 1' at the eye.
A wheel makes 360 revolutions per minute. Through how many radians does it turn in 1 second?
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.
Find the diameter of the sun in km supposing that it subtends an angle of 32' at the eye of an observer. Given that the distance of the sun is 91 × 106 km.
If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, find the ratio of their radii.
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 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
The radius of the circle whose arc of length 15 π cm makes an angle of \[\frac{3\pi}{4}\] radian at the centre is
A circular wire of radius 3 cm is cut and bent so as to lie along the circumference of a hoop whose radius is 48 cm. Find the angle in degrees which is subtended at the centre of hoop.
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.
`cos (2pi)/15 cos (4pi)/15 cos (8pi)/15 cos (16pi)/15 = 1/16`
