Question

4 cos square theta - 5 sin square theta = 5. Then find the value of sec square theta - tan square theta

Answer 1

Answer:

$4 \: {cos}^{2} \theta - 5 \: {sin}^{2} \theta = 5 \\ 4 \: {cos}^{2} \theta - 5 \: (1 - {cos}^{2} \theta ) = 5 \\ 4 \: {cos}^{2} \theta - 5 \: + 5 \: {cos}^{2} \theta = 5 \\ 9 \: {cos}^{2} \theta = 5 + 5\\ 9 \: {cos}^{2} \theta = 10\\ \implies \: {cos}^{2} \theta = \frac{10}{9} \\ \implies \: \huge \fbox{ {sec}^{2} \theta = \frac{9}{10} } \\ {tan}^{2} \theta = {sec}^{2} \theta - 1 \\ = \frac{9}{10} - 1 = \frac{9 - 10}{10} = \frac{ - 1}{10} \\\implies \huge \fbox{{tan}^{2} \theta = \frac{ - 1}{10} }\\ now \\ {sec}^{2} \theta - {tan}^{2} \theta = \frac{9}{10} - ( \frac{ - 1}{10} ) \\ = \frac{9}{10} + \frac{1}{10} = \frac{9 + 1}{10} = \frac{10}{10} = 1 \\ thus \\ \huge \fbox {{sec}^{2} \theta - {tan}^{2} \theta = 1}$

Answer 2

Answer:

Step-by-step explanation:

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