3 years ago

I NEED HELP!!!!! I am gonna be posting a lot more questions because I have been stuck on them for 2 day :(

Mathematics

1 answer:

emmainna [20.7K]3 years ago

7 0

Answer: 7. 5/4

8. 1/3

Step-by-step explanation:

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1+cos2A/cos2A = tan2A/tanA prove LHS=RHS

son4ous [18]

$RTP: \frac{1 + cos(2A)}{cos(2A)} = \frac{tan(2A)}{tan(A)}$

$LHS = \frac{1 + cos(2A)}{cos(2A)}$
$= \frac{1 + \frac{1 - tan^{2}(A)}{1 + tan^{2}(A)}}{\frac{1 - tan^{2}(A)}{1 + tan^{2}(A)}}$
$= \frac{\frac{1 + tan^{2}(A) + 1 - tan^{2}(A)}{1 + tan^{2}(A)}}{\frac{1 - tan^{2}(A)}{1 + tan^{2}(A)}}$
$= \frac{2}{1 - tan^{2}(A)}$
$= \frac{2}{1 - tan^{2}(A)} \cdot \frac{tan(A)}{tan(A)}$
$= \frac{\frac{2tan(A)}{1 - tan^{2}(A)}}{tan(A)}$
$= \frac{tan(2A)}{tan(A)}$
$= RHS$ , as required.