3. If cosec A-sin A=p and sec A- cos A= q then prove that
(p2q)2/3+ (pq2)2/3= 1
(please help )
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→ q(p 2 - 1) = 2p
→ LHS = q(p 2 - 1)
→ sec + coses [(sin + cos)] 2-1
→ ( sec + coses ) [ sin 2 + cos 2 + 2 sin. cos - 1]
→ ( 1/ cos + 1/ sin) [ 1+2sin. cis-1]
[ Identity : sin 2= cis 2=1]
taking LCM of 1/sin + 1/cos
→ ( sin + cos / sin. cos) [ 2 sin. cos]
→ sin + cos / sin. cos² sin. cos
→ 2( sin + cos )
→ 2(p) ( sin + cos =p)
Therefore , 2p = RHS
hence , 2p = 2p
I hope answer is helpful to us
is your right answer
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answer = here given cosecA-SinA=p
1/sinA-sinA=p
1-sin2A/sinA=p
cos2A/sinA=p
&also now sec
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