Advertisements
Advertisements
प्रश्न
For any angle θ, state the value of: sin2 θ + cos2 θ
उत्तर
sin2 θ =cos2 θ
= sin2 θ + 1 – sin2θ = 1
APPEARS IN
संबंधित प्रश्न
If x = 30°, verify that
(i) `\tan 2x=\frac{2\tan x}{1-\tan ^{2}x`
(ii) `\sin x=\sqrt{\frac{1-\cos 2x}{2}}`
Evaluate the following:
`(cos 45°)/(sec 30° + cosec 30°)`
State whether the following is true or false. Justify your answer.
The value of sinθ increases as θ increases.
Prove the following :
`(cos(90^@ - theta) sec(90^@ - theta)tan theta)/(cosec(90^@ - theta) sin(90^@ - theta) cot (90^@ - theta)) + tan (90^@ - theta)/cot theta = 2`
Evaluate:
`2/3 (cos^4 30° - sin^4 45°) - 3(sin^2 60° - sec^2 45°) + 1/4 cot^2 30°`.
Evaluate: `4(sin^2 30 + cos^4 60^@) - 2/3 3[(sqrt(3/2))^2 . [1/sqrt2]^2] + 1/4 (sqrt3)^2`
Evaluate: tan 7° tan 23° tan 60° tan 67° tan 83°
Evaluate: `cos 58^@/sin 32^@ + sin 22^@/cos 68^@ - (cos 38^@ cosec 52^@)/(tan 18^@ tan 35^@ tan 60^@ tan 72^@ tan 65^@)`
Without using trigonometric tables, prove that:
cos54° cos36° − sin54° sin36° = 0
Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.
sec78° + cosec56°
Prove that:
sin 60° = 2 sin 30° cos 30°
If `sqrt3` = 1.732, find (correct to two decimal place) the value of sin 60o
If A = B = 45° ,
show that:
sin (A - B) = sin A cos B - cos A sin B
Prove that:
cos 30° . cos 60° - sin 30° . sin 60° = 0
ABC is an isosceles right-angled triangle. Assuming of AB = BC = x, find the value of each of the following trigonometric ratio: cos 45°
Prove that:
4 (sin4 30° + cos4 60°) -3 (cos2 45° - sin2 90°) = 2
Given A = 60° and B = 30°,
prove that : cos (A + B) = cos A cos B - sin A sin B
If A = 30°;
show that:
(sinA - cosA)2 = 1 - sin2A
If A = 30°;
show that:
`(1 – cos 2"A")/(sin 2"A") = tan"A"`
If A = 30°;
show that:
`(1 + sin 2"A" + cos 2"A")/(sin "A" + cos"A") = 2 cos "A"`
If A = 30°;
show that:
`(cos^3"A" – cos 3"A")/(cos "A") + (sin^3"A" + sin3"A")/(sin"A") = 3`
Without using tables, evaluate the following: cosec245° sec230° - sin230° - 4cot245° + sec260°.
Prove that : cos60° . cos30° - sin60° . sin30° = 0
Prove that: `((cot30° + 1)/(cot30° -1))^2 = (sec30° + 1)/(sec30° - 1)`
Find the value of x in the following: `sqrt(3)`tan 2x = cos60° + sin45° cos45°
If A = 30° and B = 60°, verify that: `(sin("A" -"B"))/(sin"A" . sin"B")` = cotB - cotA
If A = B = 45°, verify that sin (A - B) = sin A .cos B - cos A.sin B
If sin(A - B) = sinA cosB - cosA sinB and cos(A - B) = cosA cosB + sinA sinB, find the values of sin15° and cos15°.
Find the value of the following:
(sin 90° + cos 60° + cos 45°) × (sin 30° + cos 0° – cos 45°)
If sin 30° = x and cos 60° = y, then x2 + y2 is
