Question

guys please tell me the solution...
I can't understand..​

Answer 1

Answer:

(i)

Step-by-step explanation:

cos².sec²(1-sin²=cos²)

1(cos.sec=1)

Answer 2

Answer:

$i)(1 - sin {}^{2} A)sec {}^{2} A = cos {}^{2} A \: sec {}^{2} A \\ \: \: \: \: \: = cos {}^{2}A \times \frac{1}{cos {}^{2 }A} \\ = 1$

$ii) \sqrt{sec {}^{2}Ø + cosec {}^{2}Ø} = \sqrt{ \frac{1}{cos {}^{2}Ø} + \frac{1}{sin {}^{2}Ø} } \\ \: \: \: \: \: \: = \sqrt{ \frac{sin {}^{2}Ø + cos {}^{2}Ø}{sin {}^{2}Øcos {}^{2}Ø} } \\ \: \: \: \: = \sqrt{ \frac{1}{sin {}^{2}Øcos {}^{2}Ø} } \\ \: \: \: \: = \frac{1}{sin \:Øcos \:Ø} \\ = \frac{1}{sinØ} \times \frac{1}{cosØ} \\ \: \: \: \: \: \: = cosecØsecØ...............(1) \\ tanØ + cotØ = \frac{sinØ}{cosØ} + \frac{cosØ}{sinØ} = \frac{sin {}^{2} Ø + cos {}^{2}Ø}{sinØcosØ} \\ \: \: \: \: \: \: = \frac{1}{sinØcosØ} = cosecØsecØ...........(2) \\ from \:(1) \: and \: (2) \: it \: is \: proved$

$iii)4tan {}^{2} A - \frac{4}{cos {}^{2}A } = 4(tan {}^{2}A - \frac{1}{cos {}^{2} A} ) \\ \: \: \: \: \: = 4(tan {}^{2} A - sec {}^{2}A) \\ \: \: \: \: \: \: = - 4(sec {}^{2} A- tan {}^{2} A) \\ \: \: \: \: \: \: = - 4(1) = - 4$

Sorry, rest I didn't get the answer....