Question

8. Prove that sec?0 + cosec?0 = sec?0 .cosec?0.​

Answer 1

Answer:

Step-by-step explanation:

Let us consume theta to be "p".

Now proceed.

Given, sin p - cos p = 0

=> (sin p - cos p)² = 0²

=> sin²p + cos²p = 2 sin p cos p

=> 1/2 = sin p cos p

Also, (sin p + cos p)²

= sin²p + cos²p + 2 sin p cos p

= 1 + 2 (1/2)

= 1 + 1

= 2

Therefore, (sin p + cos p) = √2

Now, sec p + cosec p = x

=> 1/cos p + 1/sin p = x

=> (sin p + cos p) / sin p cos p = x

=> 2√2 = x

Answer 2

Step-by-step explanation:

$\sec {}^{2} (x) + \csc {}^{2} (x) \\ \\ =\frac{1}{ \cos {}^{2} (x)} + \frac{1}{ \sin {}^{2} (x) } \\ \\ = \frac{{ \sin {}^{2} (x)} +{ \cos {}^{2} (x)}}{ \sin{}^{2} (x){ \cos {}^{2} (x)} } \\ \\ = \frac{1}{ \sin{}^{2} (x){ \cos {}^{2} (x)} } \\ \\ \\ = \sec {}^{2} (x) \csc {}^{2} (x)$