Question

Prove that if cot square theta + 3 cosec square theta is equals to 7 then tan theta is equal to plus or minus one

Answer 1

Step-by-step explanation:

Given:

${cot}^{2} \theta + 3 {cosec}^{2} \theta = 7 \\ \therefore \: {cot}^{2} \theta + 3 ({cot}^{2} \theta + 1) = 7\\\therefore \: {cot}^{2} \theta + 3 {cot}^{2} \theta + 3 = 7 \\ \therefore \: 4 {cot}^{2} \theta = 7 - 3 \\ \therefore \: 4 {cot}^{2} \theta = 4 \\ \therefore \: {cot}^{2} \theta = \frac{4}{4} \\ \therefore \: {cot}^{2} \theta = 1 \\ \therefore \: \frac{1}{{tan}^{2} \theta } = 1 \\ \therefore \: {tan}^{2} \theta = 1 \\ \therefore \: {tan} \theta = \pm \sqrt{1} \\ \therefore \: {tan} \theta = \pm 1 \\ thus \: proved$