Question

solve these questions​

Answer 1

1

Sin²© + Cos²© = 1

1 - Sin²© = Cos²©

1 - Cos²© = Sin²©

( the symbol © is used as theta)

Answer 2

Answer:

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Step-by-step explanation:

1-i) sin^2 theta

1-ii) cos^2 theta

1-iii) cos^2 theta

2) sec^2 x+ cosec^2 x = sec^2 x cosec^2 x

LHS = sec^2 x+ cosec^2 x

=> 1/cos^2 theta + 1/sin^2 theta

=> sin^2 theta + cos^2 theta / sin^2 theta * cos^2 theta

=> 1/sin^2 theta * 1/cos^2 theta

=> cosec^2 theta * sec^2 theta  

hence proved

3) k = sec^2 theta (1 + sin theta)(1 - sin theta)

k = sec^2 theta (1 - sin^2 theta)......... [(a+b)(a-b) = (a^2-b^2)]

k = sec^2 theta * cos^2 theta

k = 1/cos^2 theta * cos^2 theta

Cancelling cos^2 theta

=> k=1

4)

cos x = $\sqrt{1-sin^{2}x }$

sec x = 1/cosx = 1/$\sqrt{1-sin^{2}x }$

tan x = sinx/cosx = sinx/$\sqrt{1-sin^{2}x }$

cosec x = 1/sinx

cot x = cosx / sinx = $\sqrt{1-sin^{2}x }$ / sinx