Advertisements
Advertisements
प्रश्न
If A and B are complementary angles, prove that:
cot B + cos B = sec A cos B (1 + sin B)
Advertisements
उत्तर
Since, A and B are complementary angles, A + B = 90°
cot B + cos B
= cot (90° – A) + cos (90° – A)
= tan A + sin A
= `sinA/cosA + sinA`
= `(sinA + sinAcosA)/cosA`
= `(sinA(1 + cosA))/cosA`
= sec A sin A (1 + cos A)
= sec A sin (90° – B) [1 + cos (90° – B)]
= sec A cos B (1 + sin B)
APPEARS IN
संबंधित प्रश्न
If `tan theta = 12/5` find the value of `(1 + sin theta)/(1 -sin theta)`
Find the value of x, if cos x = cos 60° cos 30° – sin 60° sin 30°
Use tables to find sine of 62° 57'
Evaluate:
3 cos 80° cosec 10° + 2 cos 59° cosec 31°
Prove that:
`1/(1 + cos(90^@ - A)) + 1/(1 - cos(90^@ - A)) = 2cosec^2(90^@ - A)`
Find A, if 0° ≤ A ≤ 90° and sin 3A – 1 = 0
If 3 cot θ = 4, find the value of \[\frac{4 \cos \theta - \sin \theta}{2 \cos \theta + \sin \theta}\]
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 \[\frac{\tan 55°}{\cot 35°}\] + cot 1° cot 2° cot 3° .... cot 90°, is
2(sin6 θ + cos6 θ) – 3(sin4 θ + cos4 θ) is equal to ______.
