Advertisements
Advertisements
प्रश्न
Prove the following:
tan50° = tan40° + 2 tan10°
उत्तर
Since, 50° = 10° + 40°
∴ tan50° = tan (10° + 40°)
∴ tan50° = `(tan10^circ + tan40^circ)/(1 - tan10^circ tan40^circ)`
∴ tan50° (1 – tan10° tan40°) = tan10° + tan40°
∴ tan50° – tan10° tan40° tan50° = tan10° + tan40°
∴ tan50° – tan10° tan40° tan (90° – 40°) = tan10° + tan40°
∴ tan50° – tan10° tan40° cot40° = tan10° + tan40° ...[∵ tan(90° – θ) = cot θ]
∴ `tan50^circ - tan10^circ tan40^circ*1/tan40^circ` = tan10° + tan40°
∴ tan50° – tan10° . 1 = tan10° + tan40°
∴ tan50° = tan40° + 2 tan10°
APPEARS IN
संबंधित प्रश्न
Prove the following:
`cos (pi/2 - x) cos(pi/2 - y) - sin(pi/2 - x) sin(pi/2 - y)` = – cos (x + y)
Prove the following:
cos(x + y).cos(x − y) = cos2y − sin2x
Prove the following:
tan8θ − tan5θ − tan3θ = tan8θ · tan5θ · tan3θ
Find sin 2x, cos 2x, tan 2x if secx = `(-13)/5, pi/2 < x < pi`
If tan x = `3/4, π < x < (3π)/2`, then the value of `cos x/2` is ______.
The value of tan `π/8` is ______.
The value of `(cotx - tanx)/(cot 2x)` is ______.
