Prove the following trigonometric identities (secx+tanx)(1-sinx/cosx)=1

Mathematics

1 answer:

miss Akunina [59]3 years ago

8 0

Answer:

Below.

Step-by-step explanation:

Convert to sin's and cos's:-

(secx + tanx)(1-sinx)/cosx)

= ( 1/ cos x + sinx / cos x) * ( 1 - sin x )/ cos x)

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

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

But 1 - sin^2 x = cos^2 x

so we have

cos^2 x / cos^2 x which = 1.

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Bess [88]

<h3>Answers:</h3>

total number of pages = 550 pages

total amount of time to read the full book = 10 hours

======================================================

Work Shown:

1 hour = 55 pages

4 hours = 220 pages ... multiply both sides by 4

After 4 hours, he had read 220 pages. Since he has 330 still left to read, this brings the total to 220+330 = 550 pages overall

550/55 = 10 hours is the total amount of time needed to read the entire book at a rate of 55 pages per hour. This is assuming the rate is kept constant.

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Read 2 more answers

The function f(x) = 2x2 + 2 represents the rate of a bus traveling in miles per hour. The function g(x) = x + 2 represents the t

AlekseyPX

Answer:

(f • g)(3) = 100, the distance in miles the bus traveled

Step-by-step explanation:

The product of (miles/hour) and (hours) is (miles), so only answers with units of distance are applicable. The numbers are ...

f(3) = 2·3² +2 = 20 . . . . miles per hour

g(3) = 3+2 = 5 . . . . hours

so (f·g)(3) = f(3)·g(3) = 20·5 = 100 . . . . miles