Match the following show work to support your answer a1 bcos

Match the following (show work to support your answer)

a.-1

b.cos x

c.cot x

d. csc x

e. sex^2 x +tan^2 x

f.1

g.-tan x

h.sin x

i. sec^2 x

j. sin^2 x

1.sec x cos x=

2. sin(-x)/cos(-x)

3.tan^2 x-sec^2 x

4. 1-cos^2 x/sin x

5.cot x sin x

6. cos ^2 x(sec^2 x-1)

7. Sec^2 x-1/sin^2 x

8. sec^4 x-tan^4 x

9. cos x cot x +sin x

Solution

1.sec x cos x= (1/cosx)*cosx =1 ----(f)

2. sin(-x)/cos(-x) = -tanx ---(g)

3.tan^2 x - sec^2 x

1 +tan^2x = sec^2x

tan^2x - sec^2x = -1 ---(a)

4. (1-cos^2 x)/sin x

= sin^2x/sinx

= sinx   (h)

5.cot x sin x

= (cosx/sinx)*sinx

= cosx    (b)

6. cos ^2 x(sec^2 x-1)

= cos^2x(tan^2x)

= sin^2x   (j)

7. (Sec^2 x-1)/sin^2 x

= (1 -cos^2x)/cos^2x*sin^2x

= 1/cos^2x

=sec^2x    (i)

8. sec^4 x-tan^4 x

= (sec^2x +tan^2x)( sec^2x - tan^2x)

= (sec^2x +tan^2x) (e)

9. cos x cot x +sin x

cosx(cosx/sinx) +sinx

= ( cos^2x +sin^2x)/sinx

= 1/sinx

= cscx   (d)