Hello everyone, this is my first post to this forum! So basically, it's been a long semester in Trig and I had an A until WHAM. Trig identities really hit me hard and now my grade is almost a C. My teacher has been offering some extra credit questions and can you guys help me? I hate to be online looking for help... But these problems look nothing like the ones we had on the tests and in class... We are allowed to get tutors and help... But the math tutors at school don't know the trig so here I am... I just need some help.
I GREATLY appreciate any feedback. Here are the five questions (all over identities)
1. Prove this identity: tan2x-sec2x = tan(x-π/4)
2. Consider any triangle that does not contain a right angle. Call its angles A,B, and C. Prove that tan A + tan B + tan C = tan A ⋅ tan B ⋅ tan C
3. Prove this identity: sin^4x = 1/8(3 - 4cos2x + cos4x)
4. Prove the identity cos t ⋅ cos u ⋅ cos v = 1/4(cos(t + u + v) + cos (t +u - v) + cos(t - u - v)). Hint: begin with the right side and use cosine sum identity for three angles.
5. An exact value for cos36° can be found using the following procedure. Begin by considering sin108°. Note that 108=72+36 and use the sine sum identity. Also note that 72=2⋅36 and use double angle identities. If there are any common factors in each term, factor them out and cancel them if they are not equal to zero. You should eventually obtain a quadratic equation containing cos36°. Use the quadratic formula to obtain the exact value for cos36°. (Note that the quadratic formula should give two solutions. One can be disregarded - why?
I GREATLY appreciate any feedback. Here are the five questions (all over identities)
1. Prove this identity: tan2x-sec2x = tan(x-π/4)
2. Consider any triangle that does not contain a right angle. Call its angles A,B, and C. Prove that tan A + tan B + tan C = tan A ⋅ tan B ⋅ tan C
3. Prove this identity: sin^4x = 1/8(3 - 4cos2x + cos4x)
4. Prove the identity cos t ⋅ cos u ⋅ cos v = 1/4(cos(t + u + v) + cos (t +u - v) + cos(t - u - v)). Hint: begin with the right side and use cosine sum identity for three angles.
5. An exact value for cos36° can be found using the following procedure. Begin by considering sin108°. Note that 108=72+36 and use the sine sum identity. Also note that 72=2⋅36 and use double angle identities. If there are any common factors in each term, factor them out and cancel them if they are not equal to zero. You should eventually obtain a quadratic equation containing cos36°. Use the quadratic formula to obtain the exact value for cos36°. (Note that the quadratic formula should give two solutions. One can be disregarded - why?
