Advertisements
Advertisements
प्रश्न
Without using tables, evaluate the following: (sin90° + sin45° + sin30°)(sin90° - cos45° + cos60°).
उत्तर
(sin90° + sin45° + sin30°)(sin90° - cos45° + cos60°).
sin30° = `(1)/(2)`
sin45° = `(1)/sqrt(2)`
sin90° = 1
cos45° = `(1)/sqrt(2)`
cos60° = `(1)/(2)`
(sin90° + sin45° + sin30°)(sin90° - cos45° + cos60°)
= `(1 + 1/sqrt(2) + 1/sqrt(2))(1 - 1/sqrt(2) + 1/sqrt(2))`
= `(3/2 + 1/sqrt(2))(3/2 - 1/sqrt(2))`
= `(3/2)^2 - (1/sqrt(2))^2`
= `(9)/(4) - (1)/(2)`
= `(9 - 2)/(4)`
= `(7)/(4)`.
APPEARS IN
संबंधित प्रश्न
Find the value of x in the following :
tan 3x = sin 45º cos 45º + sin 30º
`(2 tan 30°)/(1+tan^2 30°)` = ______.
Show that tan 48° tan 23° tan 42° tan 67° = 1
Evaluate the following :
`tan 35^@/cot 55^@ + cot 78^@/tan 12^@ -1`
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
tan 65° + cot 49°
Prove that sin 48° sec 42° + cos 48° cosec 42° = 2
Prove that `sin 70^@/cos 20^@ + (cosec 20^@)/sec 70^@ - 2 cos 20^@ cosec 20^@ = 0`
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`
Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.
cosec54° + sin72°
prove that:
sin (2 × 30°) = `(2 tan 30°)/(1+tan^2 30°)`
If A =30o, then prove that :
sin 2A = 2sin A cos A = `(2 tan"A")/(1 + tan^2"A")`
If A = 30°;
show that:
sin 3 A = 4 sin A sin (60° - A) sin (60° + A)
find the value of: cosec2 60° - tan2 30°
Prove that:
cos 30° . cos 60° - sin 30° . sin 60° = 0
If `sqrt3` = 1.732, find (correct to two decimal place) the value of `(2)/(tan 30°)`
Given A = 60° and B = 30°,
prove that : cos (A + B) = cos A cos B - sin A sin B
If A = B = 45° ,
show that:
cos (A + B) = cos A cos B - sin A sin B
Without using tables, evaluate the following: sec30° cosec60° + cos60° sin30°.
Prove that: `((cot30° + 1)/(cot30° -1))^2 = (sec30° + 1)/(sec30° - 1)`
Find the value of x in the following: 2 sin3x = `sqrt(3)`
Find the value of x in the following: `sqrt(3)`tan 2x = cos60° + sin45° cos45°
If A = 30° and B = 60°, verify that: cos (A + B) = cos A cos B - sin A sin B
If A = 30° and B = 60°, verify that: `(sin("A" -"B"))/(sin"A" . sin"B")` = cotB - cotA
If A = B = 45°, verify that cos (A − B) = cos A. cos B + sin A. sin B
Verify the following equalities:
cos 90° = 1 – 2sin2 45° = 2cos2 45° – 1
If 2 sin 2θ = `sqrt(3)` then the value of θ is
