Arts (English Medium) Class 11 - CBSE Question Bank Solutions

If \[\text{ tan } x = \frac{a}{b}\], then \[b \cos 2x + a \sin 2x\]

If \[\tan\alpha = \frac{1}{7}, \tan\beta = \frac{1}{3}\], then

\[\cos2\alpha\]   is equal to

The value of `cos^2 48^@ - sin^2 12^@` is ______.

If A = cos²θ + sin⁴θ for all values of θ, then prove that `3/4` ≤ A ≤ 1.

The greatest value of sin x cos x is ______.

The value of sin 20° sin 40° sin 60° sin 80° is ______.

The value of `cos  pi/5 cos  (2pi)/5 cos  (4pi)/5 cos  (8pi)/5`  is ______.

Prove that sin 4A = 4sinA cos³A – 4 cosA sin³A

If tanθ + sinθ = m and tanθ – sinθ = n, then prove that m² – n² = 4sinθ tanθ 
[Hint: m + n = 2tanθ, m – n = 2sinθ, then use m² – n² = (m + n)(m – n)]

If tan(A + B) = p, tan(A – B) = q, then show that tan 2A = `(p + q)/(1 - pq)`

If acos2θ + bsin2θ = c has α and β as its roots, then prove that tanα + tanβ = `(2b)/(a + c)`.

`["Hint: Use the identities" cos2theta = (1 - tan^2theta)/(1 + tan^2theta) "and" sin2theta =  (2tantheta)/(1 + tan^2theta)]`.

If θ lies in the first quadrant and cosθ = `8/17`, then find the value of cos(30° + θ) + cos(45° – θ) + cos(120° – θ).

Find the value of the expression `cos^4  pi/8 + cos^4  (3pi)/8 + cos^4  (5pi)/8 + cos^4  (7pi)/8`

[Hint: Simplify the expression to `2(cos^4  pi/8 + cos^4  (3pi)/8) = 2[(cos^2  pi/8 + cos^2  (3pi)/8)^2 - 2cos^2  pi/8 cos^2  (3pi)/8]`

If tanθ = `1/2` and tanΦ = `1/3`, then the value of θ + Φ is ______.

The value of `(1 - tan^2 15^circ)/(1 + tan^2 15^circ)` is ______.

The value of cos12° + cos84° + cos156° + cos132° is ______.

The value of `sin  pi/10  sin  (13pi)/10` is ______.

`["Hint: Use"  sin18^circ = (sqrt5 - 1)/4 "and"  cos36^circ = (sqrt5 + 1)/4]`

The value of sin50° – sin70° + sin10° is equal to ______.

If sinθ = `(-4)/5` and θ lies in the third quadrant then the value of `cos  theta/2` is ______.

The value of `sin  pi/18 + sin  pi/9 + sin  (2pi)/9 + sin  (5pi)/18` is given by ______.