Question

If cosec 0 - cot 0 = root2 cotem 0 prove that
cosec0 + cot 0 = root2 cosec 0.​

Answer 1

Answer:

cosec theta + cos theta =√2 cosec theta

Step-by-step explanation:

• cosec theta =√2cot theta +cot thata
• cosec theta =(√2+1) cot theta
• cosec theta /(√2+1)= cot theta ---- (I)

Now,

cosec theta +cot theta=√2cosec theta

L.HS..

• Cosec theta + cot theta
• cosec theta+ cosec theta/(√2+1) ---- (from I)

taking LCM

• cosec theta (√2+1) + cosec theta / (√2+1)
• cosec theta(√2+1+1)/ (√2+1)
• cosec theta (√2+2)/(√2+1)
• cosec theta [√2(√2+1)] /(√2+1)
• cosec theta √2
• √2 cosec theta = RHS..