# Maths

How do I prove that

7sin^2x - sinxcosx = 6 can also be written as tan^2x + tanx - 6 = 0 ?

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. 7sin^2x - sinx cosx - 6 = 0
divide by cos^2 to get

7tan^2x - tanx - 6sec^2x = 0
7tan^2x - tanx - 6(1+tan^2x) = 0
tan^2x - tanx - 6 = 0

there's a typo, and any solutions must exclude x where cosx=0.

1. 👍
2. 👎
3. ℹ️
4. 🚩
2. working...

7sin^2x + sinxcosx = 6

sin^2x + sinxcosx= 6 - 6sin^2x
sin^2x + sinxcosx= 6(1 - sin^2x)
sin^2x + sinxcosx= 6cos^2x

divide both sides by cos^2x and you get tan^2x + tanx - 6 = 0

1. 👍
2. 👎
3. ℹ️
4. 🚩

## Similar Questions

1. ### precalculus

A weight is attached to a spring that is oscillating up and down it takes 6 sec for the spring to complete one cycle and the distance from the highest to lowest point is 7 in what equation models the position of the weight at time

2. ### Inverse trigonometry

Prove that- tan^-1(1/2tan 2A)+tan^-1(cotA)+tan^-1(cot^3A) ={0,ifpi/4

3. ### physics (speed of plane by radar)

The radar stations A and B, separated by the distance a = 500 m, track the plane C by recording the angles α and β at 1-second intervals, If three successive readings are shown in the table,calculate the speed v of the plane and

4. ### Math

Prove this identity 1. csc^2(pi/2-x)=1+sin^2xcsc^2(pi/2-x) 2. tan(pi/4+x)+tan(pi/4-x)=2sec2x

1. ### Trigonometry

Find the exact value of tan(a-b) sin a = 4/5, -3pi/2

2. ### maths --plse help me..

The angle of elevation of the top of a tower as observed from a point on the ground is alpha and on moving a meters towards the tower, the angle of elevation is beta .prove that the height of the tower is a (tan alpha*tan

3. ### trig

prove that the equation 2sin x cos x +4cos^2 x =1 may be written in the form of tan^2 x -2tan x -3=0

4. ### math

prove cos(x+y) / cos(x-y) = (1-tan x tan y)/(1+tan x tan y)

1. ### math

Prove that the equation Is an identity. Sec^4x - Tan^4x = Sec^2x + Tan^2x

2. ### Pre-Calc Help!!!

Prove the identity. (show your work please) tan(x − π/4)= (tan x − 1)/(tan x + 1) Thank you!

3. ### Trig-Weird Geometry Problem

Determine all triangles ABC for which tan(A-B)+tan(B-C)+tan(C-A)=0. There's a hint: "Can you relate A-B to B-C and C-A?" Should I apply the tangent difference formula (tan(x-y))? Help would be appreciated, thanks.

4. ### Maths

If Tan (A+B)=1/3 and Tan(A-B)=2/5,then prove that A.Tan2A=11/13 B.Tan2B=-1/17