Advertisements
Advertisements
प्रश्न
Find the value of tan 9° – tan 27° – tan 63° + tan 81°
Advertisements
उत्तर
We have tan 9° – tan 27° – tan 63° + tan 81°
= tan 9° + tan 81° – tan 27° – tan 63°
= tan 9° + tan (90° – 9°) – tan 27° – tan (90° – 27°)
= tan 9° + cot 9° – (tan 27° + cot 27°) .....(1)
Also tan 9° + cot 9° = `1/(sin 9^circ cos 9^circ)`
= `2/(sin 18^circ)` .....(2)
Similarly, tan 27° + cot 27° = `1/(sin 27^circ cos 27^circ)`
= `2/sin54^circ`
= `2/cos36^circ` .....(3)
Using (2) and (3) in (1), we get
tan 9° – tan 27° – tan 63° + tan 81° = `2/(sin18^circ) - 2/(cos36^circ)`
= `(2 xx 4)/(sqrt(5) - 1)`
= `(2 xx 4)/(sqrt(5) + 1)`
= 4
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)`
`11/16`
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`
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
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:
\[- \frac{5\pi}{6}\]
Find the degree measure corresponding to the following radian measure:
\[\left( \frac{18\pi}{5} \right)\]
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 degree measure corresponding to the following radian measure:
1c
Find the radian measure corresponding to the following degree measure: 135°
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.
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. and the number of degrees in the least angle is to the number of degrees in the mean angle as 1 : 120. Find the angles 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.
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.
A railway train is travelling on a circular curve of 1500 metres radius at the rate of 66 km/hr. Through what angle has it turned in 10 seconds?
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 D, G and R denote respectively the number of degrees, grades and radians in an angle, the
The angle between the minute and hour hands of a clock at 8:30 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
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.
Find the value of `sqrt(3)` cosec 20° – sec 20°
Prove that `(sec8 theta - 1)/(sec4 theta - 1) = (tan8 theta)/(tan2 theta)`
“The inequality `2^sintheta + 2^costheta ≥ 2^(1/sqrt(2))` holds for all real values of θ”
The value of tan1° tan2° tan3° ... tan89° is ______.
Which of the following is correct?
[Hint: 1 radian = `180^circ/pi = 57^circ30^'` approx]
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.
