Question

5tan 540°+ 2 coS 1170°+ 4 sin900— 3cos540=?​

Answer 1

Tᴏ Fɪɴᴅ :-

• 5tan 540°+ 2 coS 1170°+ 4 sin900— 3cos540=?

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

• tan180° = 0
• cos180° = (-1)
• sin180° = 0
• cos90° = 0

Sᴏʟᴜᴛɪᴏɴ :-

→ 5tan 540°+ 2 coS 1170°+ 4sin900° - 3cos540°

Putting :-

→ tan540° = tan(360°+180°) = tan180°

→ cos540° = cos(360°+180°) = cos180°

→ cos1170° = cos(3*360+90°) = cos90°

→ sin900° = sin(2*360 + 180°) = sin180°

→ 5*tan180° + 2*cos90° + 4*sin180° - 3*cos180°

Putting all Values now , we get,

→ 5*0 + 2*0 + 4*0 - 3*(-1)

→ 0 + 0 + 0 + 3

→ 3 (Ans.)

Answer 2

Solution:

☞tan540°= tan(360°+180°)= tan180°

☞cos1170° = cos(3×360°+90°)= cos90°

☞Sin900°= sin(2×360°+180°)=sin180°

☞cos540° = (360°+180°)= cos180°

✷Now,

=>5tan180°+2cos90°+4sin180°-3cos180°

=>5(0)+2(0)+4(0)-3(-1)

=>3

Rules to write down the t-ratios of an angle allied to  θ,

• Imagine  θ lies in first quadrant,even if it is not so.Now find the quadrant in which the allied angle lies and determine the sign of t-ratio in that quadrant by rule of all-sin-tan-cos.
• If the allied angle is - θ,180°± θ,360°± θ,the t-ratios remain unchanged in the form.
• If the allied is 90± θ,270± θ,the t-ratio changes as follow

1. Sin changes into cos and vice versa
2. tan changes into cot and vice versa
3. sec changes into cot and vice versa