Advertisements
Advertisements
प्रश्न
Without using trigonometric tables, prove that:
cos257° − sin233° = 0
उत्तर
LHS = cos257° − sin233°
= cos2 (`90^circ - 33^circ`) - sin2 `33^circ`
= sin2 `33^circ` - sin2 `33^circ`
= 0
= RHS
APPEARS IN
संबंधित प्रश्न
Without using trigonometric tables, evaluate
`sin^2 34^@ + sin^2 56^@ + 2tan 18^@ tan 72^@ - cot^2 30^@`
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
(sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
(cosec A - sin A) (sec A - cos A) = `1/(tanA+cotA)`
[Hint: Simplify LHS and RHS separately.]
Without using trigonometric tables, evaluate :
`sec 11^circ/("cosec" 79^circ)`
Without using trigonometric tables, evaluate :
`tan 27^circ/cot 63^circ`
Without using trigonometric tables, prove that:
tan 71° − cot 19° = 0
Without using trigonometric tables, prove that:
cos275° + cos215° = 1
Without using trigonometric tables, prove that:
sin53° cos37° + cos53° sin37° = 1
Prove that:
`cos 80^circ/(sin 10^circ) + cos 59^circ "cosec" 31^circ = 2`
Prove that:
\[\frac{\sin\theta}{\cos(90° - \theta)} + \frac{\cos\theta}{\sin(90° - \theta)} = 2\]
If A, B and C are the angles of a ΔABC, prove that tan `((C + "A")/2) = cot B/2`
A man in a boat rowing away from a lighthouse 100 m high takes 2 minutes to change the angle of elevation of the top of the lighthouse from 60° to 30°. Find the speed of the boat in metres per minute [Use `sqrt3` = 1.732]
Without using tables evaluate: `(2tan 53°)/(cot 37°) - (cot 80°)/(tan 10°)`.
Solve : Sin2θ - 3sin θ + 2 = 0 .
From the trigonometric table, write the values of tan 45°48'.
Solve the following equation: `(cos θ)/(1 - sin θ) + cos θ/(1 + sinθ) = 4`.
Solve the following equation: `(cos^2θ - 3 cosθ + 2)/sin^2θ` = 1.
The maximum value of `1/(cosec alpha)` is ______.
