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Prove that tan^2(x)=1/(cos^2(x))-1

tan^2(x)=1/(cos^2(x))-1 Left hand side of the equation (LHS)=tan^2(x) Use the identity tan(x)=sin(x)/cos(x) and substitute it into the LHS LHS=sin^2(x)/cos^2(x) Use the identity sin^2(x)+cos^2(x)=1 and rearr...
PA
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Explain why the trend in ionisation energy changes between group 5 and 6

Group 5 and 6 have a different electronic structure, with group 6 having one extra electron that group 5. If we look at Hunds rule, which states that electrons must occupy orbitals individually before pairin...
KR
Answered by Kavita R. Chemistry tutor
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f(x) = 4x^2 + 8x - 5 ; complete the square to find the turning point of f(x).

4x^2 + 8x - 5 = 0 4(x^2 + 2x - (5/4)) = 0 4((x + 1)^2 - 1^2 - (5/4)) = 0 4((x + 1)^2 - (9/4)) = 0 4(x + 1)^2 - 9 = 0 4(x + 1)^2 - 9 = 0 Turning point is at (-1, -9)
CK
Answered by Charlotte K. Maths tutor
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Solve the simultaneous equations: y=x^2+4x-2, y=x+2

Equations: 1). y=x^2+4x-2 2.)y=x+2 x+2=x^2+4x-2 First put equation 1 in equation 2 0=x^2+3x-4 Make one side of the equation equal to 0 0=(x+4)(x-1) Factorise the equations Equations 3).x+4=0 4). x-1=0 One or...
PA
Answered by Phoebe A. Maths tutor
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I'm confused about the use of the conditional tense in German, could you explain how it's formed and its uses?

The first important thing to remember about forming the conditional tense in German is that both parts of the sentence must be in the conditional tense. Take for example the sentence 'If I woke up earlier to...
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Answered by Finn P. German tutor
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