# 16 - General Trigonometry Questions Answers

Which of the following angles are co-terminal angles: 480 , -240 or 600

how can we get it which is co-terminal and what does co-terminal means?????

**Asked By: AMBUJ SINGLA**

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**Joshi sir comment**

**Coterminal angles** are angles in standard position (angles with the initial side on the positive *x*-axis) that have a common terminal side. For example 30°, –330° and 390° are all coterminal.

To find a positive and a negative angle coterminal with a given angle, you can add and subtract 360° if the angle is measured in degrees or 2π if the angle is measured in radians.

480 and -240 are co terminal angles because 480-360 = 120 and -240+360 = 120

is there any need to know or learn the proof pf formulas of trigo

**Asked By: AMBUJ SINGLA**

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**Joshi sir comment**

No, For making a good command in trigonometry, only implementation is a need. But for your knowledge you can proof these results

if x,y,z are acute and cos x= tan y , cos y = tanz , cos z = tan x, then the value of sin x is ;

**Asked By: AMIT DAS**

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**Joshi sir comment**

by 1st equation sec y = √(1+cos^{2}x) so cos y = 1/ √(1+ cos^{2}x)

by 3rd equation sec z = cot x so tan z = √(cot^{2}x - 1)

on putting these 2 values in 2nd equation we get

1/ √(1+ cos^{2}x) = √(cot^{2}x - 1)

so sin^{2}x = (1+cos^{2}x)(cos^{2}x-sin^{2}x)

or sin^{2}x = (2-sin^{2}x)(1-2sin^{2}x)

or sin^{2}x = 2-4sin^{2}x-sin^{2}x+2sin^{4}x

or 2sin^{4}x-6sin^{2}x+2 = 0

now solve it for sinx

The distance between two parallel lines is 1.A point 'A' is chosen to lie between the lines at a distance 'd' from the first line. Triangle ABC is an eqilateral triangle with 'B" on one line and 'C' on the other line.Then AB is equal to(in terms of d).

**Asked By: AMIT DAS**

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**Joshi sir comment**

In triangle BCX

BC = seca

so AB = seca

now in triangle ABY

cos(60+a) = d/seca

so 1/2 cosa - √3/2 sina = d cosa

or tana = (1-2d)/√3

now calculate seca

Find the number of solutions of the equation 2cos²(x/2)sin²(x) = x² + 1/x² , 0 < *x* ≤ π/2 .

**Asked By: HIMANSHU MITTAL**

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**Joshi sir comment**

max of sin and cos are 1 so max of left is 2

but x² + 1/x² ≥ 2x(1/x) = 2

so only solution will be obtained for 2cos²(x/2)sin²(x) = 2

so (1+cosx)(1-cos²x) = 2 which is impossible,so i think no solution

Find the value of 16cos(2π/15)cos(4π/15)cos(8π/15)cos(14π/5).

**Asked By: HIMANSHU MITTAL**

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**Joshi sir comment**

I think the last term would be cos(14π/15)

We know that cos(14π/15) = -cos(π/15)

so 16cos(2π/15)cos(4π/15)cos(8π/15)cos(14π/15)

= -16cos(π/15)cos(2π/15)cos(4π/15)cos(8π/15)

= -[8/sin(π/15)]2sin(π/15)cos(π/15)cos(2π/15)cos(4π/15)cos(8π/15)

= -[8/sin(π/15)]sin(2π/15)cos(2π/15)cos(4π/15)cos(8π/15)

take the similar steps