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# C3 trigonometry

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1. Show that:

(tanx + cot x)(sinx + cosx) = secx + cosecx
2. What have you tried?
3. i tried multiplying out the brackets and changing the tan to sin/cos and the cot to cos/sin.
then i got sin^2xsecx + sinx + cos x + cos^2xcosecx
4. so you have

Looking at the answer you know that you need

Can you combine to get that
5. (Original post by bssjonny)
i tried multiplying out the brackets and changing the tan to sin/cos and the cot to cos/sin.
then i got sin^2xsecx + sinx + cos x + cos^2xcosecx
you're almost there
write sin x = (sin^2 x) / sin x
and cos x = (cos^2 x) / cos x
then you can combine the fractions, and using (cos^2 x) + (sin^2 x) = 1 it simplifies to the other formula
6. What you need to do is find a common denominator for tan x + cot x

i.e. tanx +cot x = (sinx/cosx) + (cosx/sinx)
Cross multiply
(sinx sinx + cosx cosx)/(sinx cos x)
(sin^2 x + cos^2 x)/(sinx cosx)

finally multiply this by (sinx + cos x)
7. thanks guys, just worked it out

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