Question

If sinQ + cosQ =√2, then prove that tanQ + cotQ = 2.​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

sinQ + cosQ =√2

Squaring both sides, we get

sin²Q + cos²Q + 2sinQ cosQ = 2

1 + 2sinQ cosQ = 2

2sinQ cosQ = 1

sinQ cosQ = 1/2  ...... eqn 1

Now, tanQ + cotQ = sinQ/cosQ + cosQ/sinQ

= (sin²Q+cos²Q)/sinQcosQ  ........ [∵ taking LCM and substituting value from eqn 1]

= 1/(1/2)

= 2

∴ tanQ + cotQ = 2.​