5

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6.1.b. TRIGONOMETRIE1. S se calculeze .2. S se calculeze .

3. tiind c i c , s se calculeze .

4. tiind c i c , s se calculeze .

5. S se calculeze tg(a+b) tiind c ctg a = 2 i ctg b = 5.6. Fie astfel nct . S se calculeze .7. Fie a i b numere reale astfel nct i . S se calculeze .

8. S se determine cel mai mare element al mulimii {cos 1, cos 2, cos 3}.9. tiind c , s se arate c .

10. S se calculeze valoarea expresiei .

Rspunsuri i Indicaii

1)

2) i se aplic formula cos(a+b). Rspuns: .

3) Se nlocuiete i i din egalitatea obinut se scoate sin2x=1.

4) Se ridic la ptrat fiecare membru al egalitii. Se obine .5) ctg a = 2 . Analog . Aplicm formula tg(a+b) i obinem

6) Ducem cosx n membrul stng i procedm ca la ex 4. Rspuns: .7) Se ridic la ptrat fiecare dintre cele dou egaliti dup care se adun membru cu membru. Obinem cos(a-b) = .8) Folosim cercul trigonometric. Rspuns: cos1

9) Se trece la sin i cos i se obine uor c egalitatea este adevrat.10) 1

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