Question

cos²Q/1-tanQ + sin³Q/sinQ-cosQ = 1+ sinQ +cosQ​

Answer 1

Step-by-step explanation:

1+sin²q=3sinqcosq

Dividing both sides by cos²q, we get

1/cos²q+sin²q/cos²q=3sinqcosq/cos²q

or, sec²q+tan²q=3tanq

or, 1+tan²q+tan²q=3tanq

or, 1+2tan²q=3tanq

or, 2tan²q-3tanq+1=0

or, 2tan²q-2tanq-tanq+1=0

or, 2tanq(tanq-1)-1(tanq-1)=0

or, (tanq-1)(2tanq-1)=0

either, tanq-1=0

or, tanq=1

Or, 2tanq-1=0

or, 2tanq=1

or, tanq=1/2

∴, tanq=1 or 1/2

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Answer 2

NOTE : KINDLY REPLACE THETA BY Q