8. (a) Prove that
\[ sec \ 2A + tan \ 2A = \frac{cos \ A + sin \ A}{cos \ A - sin \ A} \]
\[ A \neq \frac{(2n + 1) \pi}{4}, \ n \in \mathbb{Z} \]
(b) Hence solve, for $0 \leq \theta < 2\pi$,
\[ sec \ 2\theta + tan \ 2\theta = \frac{1}{2} \]
Give your answers to 3 decimal places. - Edexcel - A-Level Maths Pure - Question 1 - 2015 - Paper 3
Question 1
8. (a) Prove that
\[ sec \ 2A + tan \ 2A = \frac{cos \ A + sin \ A}{cos \ A - sin \ A} \]
\[ A \neq \frac{(2n + 1) \pi}{4}, \ n \in \mathbb{Z} \]
(b) Hence sol... show full transcript
Worked Solution & Example Answer:8. (a) Prove that
\[ sec \ 2A + tan \ 2A = \frac{cos \ A + sin \ A}{cos \ A - sin \ A} \]
\[ A \neq \frac{(2n + 1) \pi}{4}, \ n \in \mathbb{Z} \]
(b) Hence solve, for $0 \leq \theta < 2\pi$,
\[ sec \ 2\theta + tan \ 2\theta = \frac{1}{2} \]
Give your answers to 3 decimal places. - Edexcel - A-Level Maths Pure - Question 1 - 2015 - Paper 3
Step 1
Prove that sec 2A + tan 2A = \frac{cos A + sin A}{cos A - sin A}
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Answer
So the final answers to the equation are:\n[ \theta \approx 2.820 , (3 , \text{decimal places}), , 5.961 , (3 , \text{decimal places}) ]
![8.-(a)-Prove-that---\[-sec-\-2A-+-tan-\-2A-=-\frac{cos-\-A-+-sin-\-A}{cos-\-A---sin-\-A}-\]---\[-A-\neq-\frac{(2n-+-1)-\pi}{4},-\-n-\in-\mathbb{Z}-\]---(b)-Hence-solve,-for-$0-\leq-\theta-<-2\pi$,---\[-sec-\-2\theta-+-tan-\-2\theta-=-\frac{1}{2}-\]---Give-your-answers-to-3-decimal-places.-Edexcel-A-Level Maths Pure-Question 1-2015-Paper 3.png](https://cdn.simplestudy.cloud/assets/backend/uploads/question/MathsPure_2015_3_1_QP_8_2015 .jpg)
