1. Verify the identity. (Simplify your answers completely.) 2.Verify the identit

ID: 3398728 • Letter: 1

Question

1. Verify the identity. (Simplify your answers completely.)

2.Verify the identity.

tan(?) + cot(?) = sec(?) csc(?)

2a. Use a Reciprocal Identity to rewrite the expression in terms of sine and cosine as a single rational expression.

2b. Then, use a Pythagorean Identity to rewrite the expression in terms of a single function, and then simplify.

3. Verfiy the identity.

(sec(t)-cos(t))/sec(t) = sin^2(t)

3a. Use a Reciprocal Identity to rewrite the expression in terms of cosine only, and then simplify.

1. 5csc(-x)/sec(-x) = -5cot(x)

LHS : we know cscx = 1/sinx ; secx = 1/cosx

cos(-x) = cosx ; sin(-x) = sinx

Now 5csc(-x)/sec(-x) = 5

-5cosx/sinx = -5cotx

2) tan + cot = sec*csc

Use a Reciprocal Identity to rewrite the expression in terms of sine and cosine as a single rational expression.

tan + cot = sec*csc

sin/cos + cos/sin = 1(cos*sin)

LHS :sin/cos + cos/sin

= (sin^2+cos^2)/sincos

= 1/sincos

= RHS

Now using pythogorean identity: 1/sincos

Use : Sin^2x +cos^2x =1 ---> cosx = sqrt( 1- sin^2x)

1/sincos = 1/sin*( 1- sin^2)^1/2

= (sin)^-1(1-sin2)^-1/2

Expressing the single function

Hence proved

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