Advertisements
Advertisements
प्रश्न
Prove that : sec245° - tan245° = 1
उत्तर
L.H.S. = sec245° - tan245°
= `(sqrt(2))^2 - (1)^2`
= 2 - 1
= 1
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Evaluate the following expression:
(i) `tan 60º cosec^2 45º + sec^2 60º tan 45º`
(ii) `4cot^2 45º – sec^2 60º + sin^2 60º + cos^2 90º.`
Evaluate the following in the simplest form: sin 60º cos 45º + cos 60º sin 45º
Evaluate the following:
`(cos 45°)/(sec 30° + cosec 30°)`
Evaluate the following:
`(sin 30° + tan 45° – cosec 60°)/(sec 30° + cos 60° + cot 45°)`
State whether the following is true or false. Justify your answer.
The value of cos θ increases as θ increases.
Prove that sin 48° sec 42° + cos 48° cosec 42° = 2
Evaluate: `(3 cos 55^@)/(7 sin 35^@) - (4(cos 70 cosec 20^@))/(7(tan 5^@ tan 25^@ tan 45^@ tan 65^@ tan 85^@))`
Prove that
cosec (67° + θ) − sec (23° − θ) = 0
Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.
sec78° + cosec56°
find the value of: sin 30° cos 30°
Prove that:
sin 60° cos 30° + cos 60° . sin 30° = 1
Prove that:
sin 60° = 2 sin 30° cos 30°
If sin x = cos y, then x + y = 45° ; write true of false
Prove that:
cos 30° . cos 60° - sin 30° . sin 60° = 0
Prove that:
cos2 30° - sin2 30° = cos 60°
prove that:
tan (2 x 30°) = `(2 tan 30°)/(1– tan^2 30°)`
ABC is an isosceles right-angled triangle. Assuming of AB = BC = x, find the value of each of the following trigonometric ratios: tan 45°
Prove that:
4 (sin4 30° + cos4 60°) -3 (cos2 45° - sin2 90°) = 2
Given A = 60° and B = 30°,
prove that: tan (A - B) = `(tan"A" – tan"B")/(1 + tan"A".tan"B")`
If A = 30°;
show that:
`(1 + sin 2"A" + cos 2"A")/(sin "A" + cos"A") = 2 cos "A"`
Without using tables, evaluate the following: sec30° cosec60° + cos60° sin30°.
Without using tables, evaluate the following: cosec245° sec230° - sin230° - 4cot245° + sec260°.
Without using tables, find the value of the following: `(sin30°)/(sin45°) + (tan45°)/(sec60°) - (sin60°)/(cot45°) - (cos30°)/(sin90°)`
Prove that: `((cot30° + 1)/(cot30° -1))^2 = (sec30° + 1)/(sec30° - 1)`
Find the value of x in the following: `sqrt(3)sin x` = cos x
Verify cos3A = 4cos3A – 3cosA, when A = 30°
Find the value of 8 sin 2x, cos 4x, sin 6x, when x = 15°
The value of `(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` is
`(2/3 sin 0^circ - 4/5 cos 0^circ)` is equal to ______.
