Question

sec square theta + cosec square theta is equal to tan theta + cot theta prove it

Answer 1

Answer:

$\red {Sec^{2}\theta + cosec^{2}\theta}$

$\green {=(tan\theta + cot\theta)^{2}}$

Step-by-step explanation:

$Sec^{2}\theta + cosec^{2}\theta \\= (1+tan^{2}\theta ) + ( 1+cot^{2}\theta)$

$\boxed { \pink { sec^{2}\theta = 1+tan^{2}theta}}$

$\boxed { \orange { cosec^{2}\theta = 1+cot^{2}theta}}$

$= tan^{2}\theta + cot^{2}\theta + 2$

$= tan^{2}\theta + cot^{2}\theta + 2tan\theta cot\theta$

$\boxed { \blue { tan\theta cot\theta = 1}}$

$= (tan\theta + cot\theta)^{2}$

$\boxed { \green { a^{2}+b^{2}+2ab = (a+b)^{2}}}$

Therefore.,

$\red {Sec^{2}\theta + cosec^{2}\theta}$

$\green {=(tan\theta + cot\theta)^{2}}$

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