Advertisements
Advertisements
Question
Without using tables, evaluate the following: sin230° sin245° + sin260° sin290°.
Solution
sin230° sin245° + sin260° sin290°
sin30° = `(1)/(2)`
sin45° = `(1)/sqrt(2)`
sin60° = `sqrt(3)/(2)`
sin90° = 1
sin230° sin245° + sin260° sin290°
= `(1/2)^2 (1/sqrt(2))^2 + (sqrt(3)/2)^2 1`
= `(1)/(4) xx (1)/(2) + (3)/(4)`
= `(1)/(8) + (3)/(4)`
= `(1 + 6)/(8)`
= `(7)/(8)`.
APPEARS IN
RELATED QUESTIONS
If θ is an acute angle and sin θ = cos θ, find the value of 2 tan2 θ + sin2 θ – 1
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.
State whether the following is true or false. Justify your answer.
sinθ = cosθ for all values of θ.
Evaluate the following :
`(sec 70^@)/(cosec 20^@) + (sin 59^@)/(cos 31^@)`
Evaluate the following :
sin 35° sin 55° − cos 35° cos 55°
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`
Prove the following
`(tan (90 - A) cot A)/(cosec^2 A) - cos^2 A =0`
Prove the following :
`(cos(90°−A) sin(90°−A))/tan(90°−A) - sin^2 A = 0`
Evaluate: Cosec (65 + θ) – sec (25 – θ) – tan (55 – θ) + cot (35 + θ)
Evaluate: `cos 58^@/sin 32^@ + sin 22^@/cos 68^@ - (cos 38^@ cosec 52^@)/(tan 18^@ tan 35^@ tan 60^@ tan 72^@ tan 65^@)`
Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.
cot65° + tan49°
Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.
sec78° + cosec56°
If sin x = cos y, then x + y = 45° ; write true of false
If A = B = 45° ,
show that:
sin (A - B) = sin A cos B - cos A sin B
find the value of: cosec2 60° - tan2 30°
find the value of: sin2 30° + cos2 30°+ cot2 45°
find the value of: cos2 60° + sec2 30° + tan2 45°
Prove that:
3 cosec2 60° - 2 cot2 30° + sec2 45° = 0
prove that:
cos (2 x 30°) = `(1 – tan^2 30°)/(1+tan^2 30°)`
Given A = 60° and B = 30°,
prove that : cos (A + B) = cos A cos B - sin A sin B
If A =30o, then prove that :
cos 2A = cos2A - sin2A = `(1 – tan^2"A")/(1+ tan^2"A")`
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: cosec330° cos60° tan345° sin290° sec245° cot30°.
Prove that: sin60°. cos30° - sin60°. sin30° = `(1)/(2)`
Prove that : cos60° . cos30° - sin60° . sin30° = 0
Find the value of x in the following: `sqrt(3)`tan 2x = cos60° + sin45° cos45°
Verify the following equalities:
sin 30° cos 60° + cos 30° sin 60° = sin 90°
Find the value of the following:
(sin 90° + cos 60° + cos 45°) × (sin 30° + cos 0° – cos 45°)
