The document Fill Ups of Trigonometric Functions & Equations, Past year Questions JEE Advance, Class 11, Maths JEE Notes | EduRev is a part of the JEE Course Maths 35 Years JEE Main & Advanced Past year Papers.

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**Q.1. Suppose sin3x.sin 3x =cos mx is an identity in x, where C _{0}, C_{1}, ___C_{n} are constants, and C_{n} ≠ 0. Then the value of n is _________. (1981 - 2 Marks)**

cos mx

sin^{3}x.sin 3x =[3 sinx – sin3x] sin 3x

=

=

= [ cos 6x + 3 cos 2x - 3 cosx - 1]

We observe that on LHS 6 is the max value of m.

∴n = 6**Q.2. The solution set of the system of equations x + y =, cosx + cosy = where x and y are real, is _________. (1987 - 2 Marks)****Ans.** φ**Sol. **The equations are x + y = 2π /3 ... (i)

cos x + cos y = 3/2 ...(ii)

From eq.

(ii)

⇒ [Using eq. (i)]

⇒

⇒

Which has no solution.

∴ The solution of given equations is φ.**Q.3. The set of all x in the interval [0,π] for which 2sin ^{2} x – 3 sin x + 1 ≥ 0, is _________. (1987 - 2 Marks)**

⇒ (2 sin x – 1) (sin x – 1) ≥ 0

⇒

But we know that sin x ≤ 1 and sin x ≥ 0 for x ∈ [0, π]

⇒ either sin x = 1 or

⇒ either x = π/2 or

Combining, we get**Q.4. The sides of a triangle inscribed in a given circle subtend angles α, β and γ at the centre. The minimum value of the arithmetic mean of and****is equal to _________. (1987 - 2 Marks)****Ans. ****Sol. **We know that A.M. ≥ G.M.

⇒ Min value of AM. is obtained when AM = GM

⇒ The quantities whose AM is being taken are equal.

i.e., Cos

⇒ sin α = sin β = sinγ

Also α +β + γ= 360° ⇒ α = β = γ=120° = 2π/3

∴ Min value of A.M.

**Q.5. The value of is equal to _________. ****(1991 - 2 Marks)****Ans. **

**Sol.**

= **Q.6. If K = sin(π/18) sin(5π/18) sin(7π/18), then the numerical value of K is _________ . (1993 - 2 Marks)****Ans. **

**Sol. **

[Using

**Q.7. If A > 0,B>0 and A + B = π/3, then the maximum value of tan A tan B is_________ . (1993 - 2 Marks)****Ans. ****Sol. **A + B = π/3 ⇒ tan (A +B ) =

[where y = tan A tan B]

⇒ tan^{2} A + (y – 1) tan A + y = 0

For real value of tan A, 3(y – 1)^{2} – 4y ≥ 0

⇒

But A, B > 0 and A + B = π/3

⇒ A, B < π/3

⇒ tan A tan B < 3

i.e., max. value of y is 1/3.**Q.8. General value of θ satisfying the equation tan ^{2}θ + sec 2θ = 1 is_________ . (1996 - 1 Mark)**

where t = tanθ

which means θ = nπ and θ =nπ±π/3

∴ cos x = 0

or x = π/2, – π/2

or cos

Now maximum value of each cos x or sin x is 1.

Hence the above equation will hold when cos x = 1 and sin x = 0. Both these imply x = 0

Hence

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