Question

AHHH PLEASE HELP MEH

Evaluate (cot90)(cos45) + sec45 exactly. No decimals allowed, rationalize if necessary

Answer 1

Answer:
`√(2)`

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Step-by-step explanation:

Rewrite each trig function terms of sine and/or cosine. Then use the unit circle to find that,

`\cot(90^(\circ))\cos(45^(\circ)) + \sec(45^(\circ))\\\\(\cos(90^(\circ)))/(\sin(90^(\circ)))\cos(45^(\circ)) + (1)/(\cos(45^(\circ)))\\\\(0)/(1)*(√(2))/(2) + (1)/((√(2))/2)\\\\(2)/(√(2))\\\\`

Now rationalize the denominator

`(2)/(√(2))\\\\(2√(2))/(√(2)*√(2))\\\\(2√(2))/(√(2*2))\\\\(2√(2))/(√(4))\\\\(2√(2))/(2)\\\\√(2)`

Which is the exact value of
`\sec(45^(\circ))`

The portion
`\cot(90^(\circ))*\cot(45^(\circ))` evaluates to 0 and goes away.