Advertisements
Advertisements
प्रश्न
Evaluate:
3 cos 80° cosec 10°+ 2 sin 59° sec 31°
उत्तर
3 cos 80° cosec 10° + 2 sin 59° sec 31°
= 3 cos 80° cosec (90° – 80°) + 2 sin 59° sec (90° – 59°)
= 3 cos 80° sec 80° + 2 sin 59° cosec 59°
= 3 × 1 + 2 × 1 ...(∵ cos A × sec A = 1)
= 3 + 2
= 5
APPEARS IN
संबंधित प्रश्न
If `cosθ=1/sqrt(2)`, where θ is an acute angle, then find the value of sinθ.
Express each of the following in terms of trigonometric ratios of angles between 0º and 45º;
(i) cosec 69º + cot 69º
(ii) sin 81º + tan 81º
(iii) sin 72º + cot 72º
Without using trigonometric tables, evaluate the following:
`(\sin ^{2}20^\text{o}+\sin^{2}70^\text{o})/(\cos ^{2}20^\text{o}+\cos ^{2}70^\text{o}}+\frac{\sin (90^\text{o}-\theta )\sin \theta }{\tan \theta }+\frac{\cos (90^\text{o}-\theta )\cos \theta }{\cot \theta }`
Solve.
sin42° sin48° - cos42° cos48°
Evaluate.
sin235° + sin255°
Show that : sin 42° sec 48° + cos 42° cosec 48° = 2
Show that : `sin26^circ/sec64^circ + cos26^circ/(cosec64^circ) = 1`
Find the value of x, if tan x = `(tan60^circ - tan30^circ)/(1 + tan60^circ tan30^circ)`
Evaluate:
`(cos75^@)/(sin15^@) + (sin12^@)/(cos78^@) - (cos18^@)/(sin72^@)`
If 4 cos2 A – 3 = 0 and 0° ≤ A ≤ 90°, then prove that sin 3 A = 3 sin A – 4 sin3 A
If 0° < A < 90°; find A, if `sinA/(secA - 1) + sinA/(secA + 1) = 2`
Write the maximum and minimum values of sin θ.
If 3 cot θ = 4, find the value of \[\frac{4 \cos \theta - \sin \theta}{2 \cos \theta + \sin \theta}\]
If 5 tan θ − 4 = 0, then the value of \[\frac{5 \sin \theta - 4 \cos \theta}{5 \sin \theta + 4 \cos \theta}\] is:
If \[\tan \theta = \frac{1}{\sqrt{7}}, \text{ then } \frac{{cosec}^2 \theta - \sec^2 \theta}{{cosec}^2 \theta + \sec^2 \theta} =\]
The value of \[\frac{\cos^3 20°- \cos^3 70°}{\sin^3 70° - \sin^3 20°}\]
Prove that:
\[\left( \frac{\sin49^\circ}{\cos41^\circ} \right)^2 + \left( \frac{\cos41^\circ}{\sin49^\circ} \right)^2 = 2\]
Prove that:
(sin θ + 1 + cos θ) (sin θ − 1 + cos θ) . sec θ cosec θ = 2
Solve: 2cos2θ + sin θ - 2 = 0.
2(sin6 θ + cos6 θ) – 3(sin4 θ + cos4 θ) is equal to ______.
