Question

If secant theta minus tan theta equal to root 3 minus 2 show that 1 minus sin theta by 1 + sin theta equal to 7 minus 4 root 3

Answer 1

Answer:

Step-by-step explanation: plz mark as brainliest

Answer 2

Answer:

The proof is explained step-wise below :

Step-by-step explanation:

$\frac{1-\sin\theta}{1+\sin\theta}=7-4\sqrt3\\\\\implies \frac{1-\sin\theta}{1+\sin\theta}\times \frac{1-\sin\theta}{1-\sin\theta}=7-4\sqrt3\\\\\implies \frac{(1-\sin\theta)^2}{1-\sin^2\theta}=7-4\sqrt3\\\\\implies (\frac{1-\sin\theta}{\cos\theta})^2=7-4\sqrt3\\\\\implies(\sec\theta-\tan\theta)^2=7-4\sqrt3.......(1)\\\\\text{Now, taking the other given equation }\\\\\sec\theta-\tan\theta=\sqrt3-2\\\\\text{squaring both the sides}\\\\\implies(\sec\theta-\tan\theta)^2=7-4\sqrt3.......(2)$

Now, using equation (1) and (2)

Hence Proved.