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Q2a) use the pythagorean identity sin(squared)t+cos(squared)t=1 to show that tan(squared)t= sec(squared)t-1sin2t+cos2t=1→ sin2t=1-cos2ttant=sintcost → tan2t=sin2tcos2tsect=1cost→sec2t=1cos2tsec2t-1=1cos2t-1=1cos2t-cos2tcos2t=1-cos2tcos2t=sin2tcos2t=tan2tb) use the sum or difference formulas to find the exact value for cos pie/12π3-π4=4π12-3π12=π12cosπ12=cosπ3-π4=cosπ3cosπ4+sinπ3sinπ412?22+32?22=6+24≈0.9659c) a vector force of 112 newton acts in a direction inclined at 48degrees to the vertical. find the magnitude of the components in the horizontal and vertical directionsd) two two-dimensional vectors are v1= and v2=. find the angle between them in degrees There was no information about v1 and v2. Perhaps it was cut off when you posted. It should look something like this: v1=[1, 3] or v1=[1 3] or v1=1i +3j or v1=1x + 3yIf you have more detail, please repost and I will provide the answer. All of your questions had numerical inputs and answers. If on the off chance your class/teacher is asking for the algebra solution for any two vectors v1 and v2 then the answer is found by rearranging this formula:v1?v2=|v1||v2|cos (θ)where v1?v2 is the dot product of v1 and v2and |v1|, |v2| are the magnitudes of v1 and v2θ=cos-1 (v1?v2/|v1||v2|)I highly doubt this is the answer your teacher is looking for. ................
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