Advertisements
Advertisements
प्रश्न
Without using trigonometric tables, prove that:
cos275° + cos215° = 1
उत्तर
LHS = cos275° + cos215°
= cos2(`90^circ - 15^circ) + cos^2 15^circ`
= `sin^2 15^circ + cos^2 15^circ`
= 1
= 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:
(cosec A - sin A) (sec A - cos A) = `1/(tanA+cotA)`
[Hint: Simplify LHS and RHS separately.]
Without using trigonometric tables, evaluate :
`cos 35^circ/sin 55^circ`
Without using trigonometric tables, prove that:
tan 71° − cot 19° = 0
Without using trigonometric tables, prove that:
tan266° − cot224° = 0
Without using trigonometric tables, prove that:
sin248° + sin242° = 1
Without using trigonometric tables, prove that:
sin53° cos37° + cos53° sin37° = 1
Without using trigonometric tables, prove that:
sin35° sin55° − cos35° cos55° = 0
Prove that:
`(sin 70^circ)/(cos 20^circ) + ("cosec" 20^circ)/(sec 70^circ) - 2 cos 70^circ "cosec" 20^circ = 0`
Prove that:
`(2 "sin" 68^circ)/(cos 10^circ )- (2 cot 15^circ)/(5 tan 75^circ) = ((3 tan 45^circ t an 20^circ tan 40^circ tan 50^circ tan 70^circ)) /5= 1`
If A, B and C are the angles of a ΔABC, prove that tan `((C + "A")/2) = cot B/2`
If tan 2 A = cot (A − 12°), where 2 A is an acute angle, find the value of A.
Prove that `(sin "A" - cos "A" + 1)/(sin "A" + cos "A" - 1) = 1/(sec "A" - tan "A")`
Prove the following:
`1/(1+sin^2theta) + 1/(1+cos^2theta) + 1/(1+sec^2theta) + 1/(1+cosec^2theta) = 2`
Given that `tan (θ_1 + θ_2) = (tan θ_1 + tan θ_2)/(1 - tan θ_1 tan θ_2)` Find (θ1 + θ2) when tan θ1 = `1/2 and tan θ_2 = 1/3`.
From the trigonometric table, write the values of cos 23°17'.
Solve the following equation: `(cos θ)/(1 - sin θ) + cos θ/(1 + sinθ) = 4`.
`(sin 20°50' + tan 67°40')/(cos 32°20' - sin 15°10')`