PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions

Reduce each of the following expressions to the sine and cosine of a single expression: 

24 cos x + 7 sin x 

Show that sin 100° − sin 10° is positive. 

Prove that \[\left( 2\sqrt{3} + 3 \right) \sin x + 2\sqrt{3} \cos x\]  lies between \[- \left( 2\sqrt{3} + \sqrt{15} \right) \text{ and } \left( 2\sqrt{3} + \sqrt{15} \right)\]

If α + β − γ = π and sin² α +sin² β − sin² γ = λ sin α sin β cos γ, then write the value of λ. 

If x cos θ = y cos \[\left( \theta + \frac{2\pi}{3} \right) = z \cos \left( \theta + \frac{4\pi}{3} \right)\]then write the value of \[\frac{1}{x} + \frac{1}{y} + \frac{1}{z}\] 

Write the maximum and minimum values of 3 cos x + 4 sin x + 5. 

Write the maximum value of 12 sin x − 9 sin² x. 

If 12 sin x − 9sin² x attains its maximum value at x = α, then write the value of sin α.

Write the interval in which the value of 5 cos x + 3 cos \[\left( x + \frac{\pi}{3} \right) + 3\] lies. 

If tan (A + B) = p and tan (A − B) = q, then write the value of tan 2B. 

If \[\frac{\cos \left( x - y \right)}{\cos \left( x + y \right)} = \frac{m}{n}\]  then write the value of tan x tan y. 

If a = b \[\cos \frac{2\pi}{3} = c \cos\frac{4\pi}{3}\] then write the value of ab + bc + ca.  

If A + B = C, then write the value of tan A tan B tan C.

If sin α − sin β = a and cos α + cos β = b, then write the value of cos (α + β). 

If tan \[\alpha = \frac{1}{1 + 2^{- x}}\] and \[\tan \beta = \frac{1}{1 + 2^{x + 1}}\] then write the value of α + β lying in the interval \[\left( 0, \frac{\pi}{2} \right)\] 

The value of \[\sin^2 \frac{5\pi}{12} - \sin^2 \frac{\pi}{12}\] 

If A + B + C = π, then sec A (cos B cos C − sin B sin C) is equal to

tan 20° + tan 40° + \[\sqrt{3}\] tan 20° tan 40° is equal to 

If \[\tan A = \frac{a}{a + 1}\text{ and } \tan B = \frac{1}{2a + 1}\] 

If 3 sin x + 4 cos x = 5, then 4 sin x − 3 cos x =