The first question, i don’t know how to do it.

see explanation

Step-by-step explanation:

(a)

using the trigonometric identity

• sec x = , then

7cos x - 3 = 2cos²x ( arrange in standard form )

2cos²x - 7cosx + 3 = 0 ← in standard form

we require the factors of the product 2 × 3 = 6 which sum to - 7

these are - 6 and - 1

use these factors to split the middle term

2cos²x - 6cosx - cosx + 3 = 0 ( factor by grouping )

2cosx(cosx - 3) - 1(cosx - 3) = 0 ( factor out (cosx - 3) )

(cosx - 3)(2cosx - 1) = 0

equate each factor to zero and solve for x

cosx - 3 = 0 ⇒ cosx = 3 ← has no solution

2cosx - 1 = 0 ⇒ cosx = ⇒ x = 60° , x = 300°

solution x = 60°, x = 300° for 0° < x < 360°

(b)

using the trigonometric identity

• cos2x = 1 - 2sin²x, then

1 - 2sin²x - 3sinx - 1 = 0 ← in standard form

- 2sin²x - 3sinx = 0 ( multiply through by - 1 )

2sin²x + 3sinx = 0 ( factor out sinx )

sinx(2sinx + 3) = 0

equate each factor to zero and solve for x

2sinx + 3 = 0 ⇒ sin x = - ← has no solution

sinx = 0 ⇒ x = 180°

solution x = 180° for 0° < x < 360°

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

160 cm

step-by-step explanation:

you have to add all the sides together