Question

If sec 34° = x then find the value of cot2 56° + cosec 56°. please answer it​

Answer 1

Answer:

$\red { Value \: of \: cot^{2} 56\degree + cosec^{2} 56\degree }$

$\green {=2x^{2} - 1 }$

Step-by-step explanation:

$Given \: sec 34\degree = x \: ---(1)$

$Value \: of \: cot^{2} 56\degree + cosec^{2} 56\degree \\= cot^{2} (90- 34)\degree + cosec^{2} (90-34)\degree \\= tan^{2} 34\degree + sec^{2} 34\degree \\= (sec^{2} 34\degree - 1 ) + sec^{2} 34\degree$

$\boxed { \pink { tan^{2} A = sec^{2} A - 1 }}$

$= 2sec^{2} 34\degree - 1 \\=2x^{2} - 1 \: [from \:(1) ]$

Therefore.,

$\red { Value \: of \: cot^{2} 56\degree + cosec^{2} 56\degree }$

$\green {=2x^{2} - 1 }$

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