Advertisements
Advertisements
प्रश्न
Prove that `2 sin^2 (3pi)/4 + 2 cos^2 pi/4 + 2 sec^2 pi/3` = 10
Advertisements
उत्तर
`sin (3pi)/4 = sin 3 xx 45^circ = sin 135^circ`
= sin (180 - 45)
= sin 45° = `1/sqrt2`
`sec ((pi/3)) = 2`
`therefore 2 sin^2 ((3pi)/4) + 2 cos^2 pi/4 + 2 sec^2 pi/3`
`= 2 (sin (3pi)/4)^2 + 2 (cos pi/4)^2 + 2 (sec pi/3)^2`
`= 2 (1/sqrt2)^2 + 2 (1/sqrt2)^2 + 2 (2)^2`
`= cancel(2)(1/cancel(2)) + cancel(2)(1/cancel(2)) + 2 (2)^2`
= 1 + 1 + 8 = 10
Hence proved.
APPEARS IN
संबंधित प्रश्न
Find the value of the following:
cosec 15º
Find the value of the following:
cot 75°
Find the value of the following:
`sin pi/4 cos pi/12 + cos pi/4 sin pi/12`
Prove that cot 4x (sin 5x + sin 3x) = cot x(sin 5x - sin 3x).
The value of sin 15° is:
The value of sin 28° cos 17° + cos 28° sin 17°
The value of sec A sin(270° + A) is:
The value of cos2 45° – sin2 45° is:
The value of 4 cos3 40° – 3 cos 40° is
If tan A = `1/2` and tan B = `1/3` then tan(2A + B) is equal to:
