Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Core 3 trig identities help

can anyone help me with 8c and 8d?

http://store.aqa.org.uk/qual/gceasa/qp-ms/AQA-MPC3-W-QP-JUN07.PDF

8c i dont understand how to simplify the 2tanxcotx like they did in the mark scheme, and 8d i dont get what they did in the first part when they turned it into sec^2 x and cosec^2 x

(tan x + cotx)^2 = tan^2x + cot^2x + 2cotxtanx

cotx = \frac{1}{tanx}

therefore:

tan^2 x + cot^2x + \dfrac{2tanx}{tanx}

tanx cancel out, replace the other 2 with the trig functions and the +2 goes as well.

isnt 2tanxcotx simplified to 2?

For 8d. use your answer from part c, that's what the "hence" means.

\displaystyle \int^1_{0.5} sec^2x + cosec^2x \ dx = \left[tanx - cotx \right]^1_{0.5}

stick the numbers in, answer!

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